Sequences

a(n) = 5*binomial(n, 6).

a(n) = (2n+3)! /( n! * (n+1)! ).

Expansion of (sqrt(1-4x^2) - sqrt(1-4x))/(2x).

Number of bond-rooted polyenoids with n edges.

Stirling numbers of the first kind: s(n+2, n).

Stirling numbers of first kind s(n+4, n).

a(2n) = n+2, a(2n-1) = smallest number requiring n+2 letters in English.

a(n) = (2n+3)!/(n!*(n+2)!).

a(n) = 2^n - 2.

a(n) = 4^n - C(4,3)*3^n + C(4,2)*2^n - C(4,1).

Differences of 0: 6!*Stirling2(n,6).

Primes p of the form 3k+1 such that Sum_{x=1..p} cos(2*Pi*x^3/p) > sqrt(p).

Primes p of the form 3k+1 such that -sqrt(p) < sum_{x=1..p} cos(2*Pi*x^3/p) < sqrt(p).

Primes p of the form 3k+1 such that sum_{x=1..p} cos(2*Pi*x^3/p) < -sqrt(p).

Class number of Q(sqrt(-n)), n squarefree.

Number of ordered ways of writing n as a sum of 2 squares of nonnegative integers.

Euler's "numerus idoneus" (or "numeri idonei", or idoneal, or suitable, or convenient numbers).

"First factor" (or relative class number) h- for cyclotomic field Q( exp(2 Pi / prime(n)) ).

Irregular primes: primes p such that at least one of the numerators of the Bernoulli numbers B_2, B_4, ..., B_{p-3} (A000367) is divisible by p.

Dimension of the n-th graded piece of the mod-2 Steenrod algebra A_2.

Narayana's cows sequence: a(0) = a(1) = a(2) = 1; thereafter a(n) = a(n-1) + a(n-3).

Padovan sequence (or Padovan numbers): a(n) = a(n-2) + a(n-3) with a(0) = 1, a(1) = a(2) = 0.

a(n) = a(n-1) + n*a(n-2); a(0) = a(1) = 1.

Genus of complete graph on n nodes.

Chromatic number (or Heawood number) Chi(n) of surface of genus n.

Number of free planar polyenoids with 2n nodes and symmetry point group C_{2h}.

Number of free planar polyenoids with n nodes and symmetry point group C_{2v}.

Length of longest simple cycle without chords in the n-dimensional hypercube graph. Also called n-coil or closed n-snake-in-the-box problem.

Number of collinear point-triples in an n X n grid.

Number of inequivalent n-gons.

Number of n-gons with n vertices.

Number of free planar polyenoids with n nodes and symmetry point group C_s.

Number of free planar polyenoids with n nodes.

Number of combinatorial types of simplicial n-dimensional polytopes with n+3 nodes.

Number of polyhedra (or 3-connected simple planar graphs) with n nodes.

Euclid-Mullin sequence: a(1) = 2, a(n+1) is smallest prime factor of 1 + Product_{k=1..n} a(k).

Euclid-Mullin sequence: a(1) = 2, a(n+1) is the largest prime factor of 1 + Product_{k=1..n} a(k).

Number of free nonplanar polyenoids with n nodes and symmetry point group C_{2v}.

Number of free nonplanar polyenoids with n nodes and symmetry point group C_s.

Number of forests with n nodes and height at most 2.

Number of forests with n nodes and height at most 3.

Number of forests with n nodes and height at most 4.

Numbers k == 2 (mod 4) that are the orders of conference matrices.

Number of free nonplanar polyenoids with n nodes.

Conjecturally largest even integer which is an unordered sum of two primes in exactly n ways.

A sequence satisfying (a(2n+1) + 1)^3 = Sum_{k=1..2n+1} a(k)^3.

A sequence satisfying (a(2n+1) + 1)^3 = Sum_{k=1..2n+1} a(k)^3.

Fine's sequence (or Fine numbers): number of relations of valence >= 1 on an n-set; also number of ordered rooted trees with n nodes having root of even degree.

Number of ordered rooted trees with n edges having root of odd degree.

Lucky numbers.