Sequences

Number of Boolean functions of n variables.

Number of partitions into non-integral powers.

Coefficients of ménage hit polynomials.

Number of partitions into non-integral powers.

Number of partitions of n into 2 squares.

Number of 3-dimensional polyominoes (or polycubes) with n cells.

Series-parallel numbers.

Number of partitions of n into 3 squares (allowing part zero).

Double factorial of even numbers: (2n)!! = 2^n*n!.

Subfactorial or rencontres numbers, or derangements: number of permutations of n elements with no fixed points.

Nearest integer to modified Bessel function K_n(2).

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

Number of labeled rooted trees with n nodes: n^(n-1).

Number of ways of placing n nonattacking queens on an n X n board.

Number of self-complementary graphs with n nodes.

The Franel number a(n) = Sum_{k = 0..n} binomial(n,k)^3.

Unitary-sociable numbers (smallest member of each cycle).

Number of partitions of n into 5 squares.

Related to zeros of Bessel function.

Generalized tangent numbers d_(n,2).

Number of partitions of n into 6 squares.

Superfactorials: product of first n factorials.

Ménage numbers: a(0) = 1, a(1) = -1, and for n >= 2, a(n) = number of permutations s of [0, ..., n-1] such that s(i) != i and s(i) != i+1 (mod n) for all i.

Expansion of E.g.f. exp(-x)/(1-3x).

Coefficients of ménage hit polynomials.

Tangent (or "Zag") numbers: e.g.f. tan(x), also (up to signs) e.g.f. tanh(x).

Number of discordant permutations of length n.

Number of genus 0 rooted maps with 3 faces with n vertices.

Coefficients of ménage hit polynomials.

Number of 3 X n Latin rectangles in which the first row is in order.

Generalized Euler numbers, c(5,n).

(1) Number of solutions to x^2 == 0 (mod n). (2) Also square root of largest square dividing n. (3) Also max_{ d divides n } gcd(d, n/d).

Number of solutions to x^3 == 0 (mod n).

Number of solutions to x^4 == 0 (mod n).

Generalized tangent numbers d(3, n).

Generalized Euler numbers c(6,n).

Nearest integer to log n.

n appears 2n times, for n >= 1; also nearest integer to square root of n.

a(n) = floor(log(n)).

Integer part of square root of n. Or, number of positive squares <= n. Or, n appears 2n+1 times.

a(n) = (n!)!.

Largest order of automorphism group of a tournament with n nodes.

Coefficient of q^(2n-1) in the series expansion of Ramanujan's mock theta function f(q).

Number of bicentered hydrocarbons with n atoms.

Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622.

a(8i+j) = 13i + a(j), where 1<=j<=8.

a(n) = sigma(n), the sum of the divisors of n. Also called sigma_1(n).

Lucas numbers (beginning with 1): L(n) = L(n-1) + L(n-2) with L(1) = 1, L(2) = 3.

Number of positive integers <= 2^n of form x^2 + 3 y^2.

Even sequences with period 2n.