Sequences

Nearest integer to exponential integral of n.

Coefficients of Legendre polynomials.

Coefficients of Legendre polynomials.

Coefficients of Legendre polynomials.

Hertzsprung's problem: ways to arrange n non-attacking kings on an n X n board, with 1 in each row and column. Also number of permutations of length n without rising or falling successions.

Number of ways to place n nonattacking bishops on an n X n board.

A jumping problem.

The game of Mousetrap with n cards (given n letters and n envelopes, how many ways are there to fill the envelopes so that at least one letter goes into its right envelope?).

The game of Mousetrap with n cards: the number of permutations of n cards having at least one hit after 2.

The game of Mousetrap with n cards: the number of permutations of n cards in which 2 is the only hit.

Glaisher's function W(n).

Number of partitions of n into a prime and a square.

Number of pairs x,y such that y-x=2, (x,n)=1, (y,n)=1 and 1 <= x <= n.

7-smooth numbers: positive numbers whose prime divisors are all <= 7.

Denominators of coefficients of odd powers of x of the expansion of Bessel function J_1(x).

Numbers k such that x^k + x + 1 is irreducible over GF(2).

Primes of the form 6m + 1.

Wonderful Demlo numbers: a(n) = ((10^n - 1)/9)^2.

Bisection of A000930.

Numbers of the form x^2 + 2*y^2.

Numbers of the form 2x^2 + 3y^2.

Numbers of form x^2 + 6y^2.

Theta series of Borcherds' 27-dimensional unimodular lattice U_27.

Expansion of Jacobi theta function {theta_1}'(q) in powers of q^(1/4).

Number of ménage permutations.

Numerators of convergents to Pi.

Apart from two leading terms (which are present by convention), denominators of convergents to Pi (A002485 and A046947 give numerators).

Stern's diatomic series (or Stern-Brocot sequence): a(0) = 0, a(1) = 1; for n > 0: a(2*n) = a(n), a(2*n+1) = a(n) + a(n+1).

a(n) = n^(n^n).

a(n) = n^(n^2), or (n^n)^n.

Theta series of 27-dimensional unimodular lattice with root system A_1 and a parity vector of norm 3.

Smallest number of stones in Tchoukaillon (or Mancala, or Kalahari) solitaire that make use of n-th hole.

Sum of the first n even squares: a(n) = 2*n*(n+1)*(2*n+1)/3.

Number of ways to arrange n non-attacking kings on an n X n board, with 2 sides identified to form a cylinder, with 1 in each row and column.

Number of n-node graphs without isolated nodes.

Theta series of 27-dimensional unimodular lattice with root system A_1 with no parity vector of norm 3.

Primes of the form k^2 + 1.

Numbers N in A002809 such that there is rho > 0 such that for all A > 0, A008475(A)-A008475(N) >= rho*log(A/N).

Related to a highly composite sequence (A002497).

Number of self-converse digraphs with n nodes.

Number of self-converse relations on n points.

a(n) = 7^n - 3*4^n + 2*3^n.

Number of connected relations.

Numbers k such that binomial(2*k,k) is divisible by (k+1)^2.

Numbers x such that 1 + 3*x*(x-1) is a ("cuban") prime (cf. A002407).

Nearest integer to the n-th Gram point.

Denominators of coefficients of expansion of Bessel function J_2(x).

Expansion of a modular function for Gamma_0(6).

Expansion of a modular function for Gamma_0(6).

Expansion of a modular function for Gamma_0(14).