Sequences

sigma_5(n), the sum of the 5th powers of the divisors of n.

Numbers containing an even number of letters.

Numbers containing an odd number of letters.

Stirling's formula: numerators of asymptotic series for Gamma function.

Stirling's formula: denominators of asymptotic series for Gamma function.

Position of first even digit after decimal point in sqrt(n).

Smallest natural number requiring n letters in English.

Smallest natural number requiring n words in English (as spoken in England).

Number of fixed polyominoes with n cells.

Number of board-pile polyominoes with n cells.

Number of board-pair-pile polyominoes with n cells.

From least significant term in expansion of E( tr (X'*X)^n ), X rectangular and Gaussian. Also number of types of sequential n-swap moves for traveling salesman problem.

Smallest even number that is an unordered sum of two odd primes in exactly n ways.

Half the number of binary relations on n unlabeled points.

Number of oriented graphs (i.e., digraphs with no bidirected edges) on n unlabeled nodes. Also number of complete digraphs on n unlabeled nodes. Number of antisymmetric relations (i.e., oriented graphs with loops) on n unlabeled nodes is A083670.

Pisano periods (or Pisano numbers): period of Fibonacci numbers mod n.

Number of zeros in fundamental period of Fibonacci numbers mod n.

Fibonacci entry points: a(n) = least k >= 1 such that n divides Fibonacci number F_k (=A000045(k)).

Fibonacci frequency of n.

Leonardo logarithm of n.

Erroneous version of A002572.

Number of Baxter permutations of length n (also called Baxter numbers).

Number of cells of square lattice of edge 1/n inside quadrant of unit circle centered at 0.

Number of nontrivial Baxter permutations of length 2n-1.

Number of simple Hamiltonian paths connecting opposite corners of a 2n+1 X 2n+1 grid.

Number of nontrivial Baxter permutations of length 2n-1.

Number of cubic Hamiltonian graphs with 2n nodes.

Number of connected labeled graphs with n nodes.

Number of even graphs with n edges.

Number of degree-n permutations of order exactly 2.

Wedderburn-Etherington numbers: unlabeled binary rooted trees (every node has outdegree 0 or 2) with n endpoints (and 2n-1 nodes in all).

Digits of positive squares.

Number of full sets of size n.

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

a(n) = A059366(n,n-2) = A059366(n,2) for n >= 2, where the triangle A059366 arises in the expansion of a trigonometric integral.

a(n) = floor(n*log((14/11)*n^(10/9))).

Double-bitters: only even length runs in binary expansion.

Zarankiewicz's problem k_2(n).

Zarankiewicz's problem k_3(n).

Erroneous version of A056642.

Number of linear geometries on n (unlabeled) points.

Number of Steiner triple systems (STS's) on 6n+1 or 6n+3 elements.

a(1)=0, a(2n) = a(n)+1, a(2n+1) = 10*a(n+1).

Simple continued fraction expansion of Pi.

Continued fraction for e^2.

Number of clouds with n points; number of undirected 2-regular labeled graphs; or number of n X n symmetric matrices with (0,1) entries, trace 0 and all row sums 2.

Number of self-dual monotone Boolean functions of n variables.

Number of fixed hexagonal polyominoes with n cells.

a(n) = solution to the postage stamp problem with 3 denominations and n stamps.

a(n) is the solution to the postage stamp problem with 4 denominations and n stamps.