Sequences

Almost trivalent maps.

a(n) = 4*(2n+1)!/n!^2.

Almost trivalent maps.

Number of filaments with n square cells.

Number of symmetric filaments (strip polyominoes) with n square cells.

a(n) = n^2 reduced mod 100.

Number of first n tetrahedral numbers (A000292) that are relatively prime to n.

Expansion of e.g.f. exp(sin(x)).

From a distribution problem.

a(n) = a(n-1) - (n-1)(n-2)a(n-2).

a(n+1) = a(n) - n*(n-1)*a(n-1), with a(n) = 1 for n <= 3.

Pile of coconuts problem: (n-1)*(n^n - 1), n even; n^n - n + 1, n odd.

In the pile of coconuts problem, the number of coconuts that remain to be shared equally at the end of the process.

a(n) = 6*4^n.

k appears k times; a(n) = floor(sqrt(2n) + 1/2).

Smaller of an amicable pair: (a,b) such that sigma(a) = sigma(b) = a+b, a < b.

Generalized ballot numbers (first differences of Motzkin numbers).

Number of connected graphs on n labeled nodes, each node being colored with one of 2 colors, such that no edge joins nodes of the same color.

Number of connected graphs on n labeled nodes, each node being colored with one of 3 colors, such that no edge joins nodes of the same color.

Number of connected graphs on n labeled nodes, each node being colored with one of 4 colors, such that no edge joins nodes of the same color.

Number of connected graphs on n labeled nodes, each node being colored with one of 5 colors, such that no edge joins nodes of the same color.

Number of labeled connected digraphs on n nodes where every node has indegree 0 or outdegree 0 and no isolated nodes.

Number of n-colored connected graphs on n labeled nodes.

Number of perfect partitions of n.

Kempner numbers: smallest positive integer m such that n divides m!.

Numbers that contain primes to odd powers only.

Compressed primes: a(n) is the nearest integer to prime(n)/log prime(n).

Product of all primes up to 3^n.

Numbers dividing A002037(i) and larger than A002037(i-1), for some i>0.

Convolution inverse of A143348.

Related to partitions.

Expansion of x/((1-x)(1-4x^2)(1-5x)).

a(n) = 7*4^n.

MacMahon's solid partitions of n in which 2 is the smallest summand.

MacMahon's solid partitions of n in which 3 is the smallest summand.

MacMahon's solid partitions of n in which 4 is the smallest summand.

Larger of amicable pair.

Number of 3 X (2n+1) zero-sum arrays with entries -n,...,0,...,n.

Segmented numbers, or prime numbers of measurement.

Prime numbers of measurement.

Number of simplices in barycentric subdivision of n-simplex.

Steffensen's bracket function [n,2].

Prime determinants of forms with class number 2.

a(n) = least value of m for which Liouville's function A002819(m) = -n.

Binomial coefficient C(2n+1, n-1).

Number of diagonal dissections of a convex n-gon into n-4 regions.

Number of diagonal dissections of a convex n-gon into n-5 regions.

Fourth convolution of Catalan numbers: a(n) = 4*binomial(2*n+3,n)/(n+4).

Number of internal triangles in all triangulations of an (n+1)-gon.

Number of partitions of an n-gon into (n-4) parts.