In combinatorics, the Eulerian number A ( n , k ) {\textstyle A(n,k)} is the number of permutations of the numbers 1 to n {\textstyle n} in which exactly...

In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices)...

node 2034 - number of unlabeled graphs on 11 nodes whose components are unicyclic graphs 2035 – Wolstenholme number 2036 – Eulerian number 2039 – Sophie...

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that...

OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A008517 (Second-order Eulerian triangle T(n, k), 1 <= k <= n)". The On-Line Encyclopedia of Integer Sequences...

the Euler diagram shows only relevant relationships. The first use of "Eulerian circles" is commonly attributed to Swiss mathematician Leonhard Euler (1707–1783)...

month, the number of pairs of rabbits is equal to the number of mature pairs (that is, the number of pairs in month n – 2) plus the number of pairs alive...

the union of k ascending runs. The number of permutations of n with k ascents is (by definition) the Eulerian number ⟨ n k ⟩ {\displaystyle \textstyle...

A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has...

26 sporadic simple groups. Sloane, N. J. A. (ed.). "Sequence A000295 (Eulerian numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation...

the number 1 differently than larger numbers, sometimes even not as a number at all. Euclid, for example, defined a unit first and then a number as a...

mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer...

hundred [and] eighty-four) is the natural number following 183 and preceding 185. There are 184 different Eulerian graphs on eight unlabeled vertices, and...

have even degree. All Eulerian circuits are also Eulerian paths, but not all Eulerian paths are Eulerian circuits. Euler's work was presented to the St...

In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number...

}}={\frac {120}{5040}}={\frac {1}{42}}} There are formulas connecting Eulerian numbers ⟨n m⟩ to Bernoulli numbers: ∑ m = 0 n ( − 1 ) m ⟨ n m ⟩ = 2 n +...

In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance...

Delannoy number Eulerian number Hypergeometric function List of factorial and binomial topics Macaulay representation of an integer Motzkin number Multiplicities...

an Eulerian poset is a graded poset in which every nontrivial interval has the same number of elements of even rank as of odd rank. An Eulerian poset...

decomposition. Define an Eulerian graph as a graph with an Eulerian cycle. Every Eulerian graph is bridgeless. This is because in an Eulerian graph every edge...

In mathematics, a harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic...

In mathematics, a double Mersenne number is a Mersenne number of the form M M p = 2 2 p − 1 − 1 {\displaystyle M_{M_{p}}=2^{2^{p}-1}-1} where p is prime...

discrete mathematics, the BEST theorem gives a product formula for the number of Eulerian circuits in directed (oriented) graphs. The name is an acronym of...

In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon: 2-3 . These are one type of 2-dimensional figurate...

highly composite number is a positive integer that has more divisors than all smaller positive integers. If d(n) denotes the number of divisors of a positive...

In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that...

triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples...

html Weisstein, Eric W. "Eulerian Number." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/EulerianNumber.html Weisstein, Eric W....

In number theory, a Carmichael number is a composite number ⁠ n {\displaystyle n} ⁠ which in modular arithmetic satisfies the congruence relation: b n...

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with...