Sequences

Number of Latin squares of order n; or labeled quasigroups.

Number of connected functions (or mapping patterns) on n unlabeled points, or number of rings and branches with n edges.

Number of nonisomorphic connected functions with no fixed points, or proper rings with n edges.

Number of prime knots with n crossings.

Number of alternating prime knots with n crossings.

Number of partitions of n that do not contain 1 as a part.

a(0) = 1; for n > 0, a(n) = 2^(n-1)*n!.

a(n) = binomial(n,floor(n/2))*(n+1)!.

Largest number in n-th row of triangle of Lah numbers (A008297 and A271703).

Largest number in n-th row of triangle A019538.

Largest Stirling numbers of second kind: a(n) = max_{k=1..n} S2(n,k).

a(n) = max_{k=0..n} 2^k*A048993(n,k).

Number of partitions of {1..2n} that are invariant under a permutation consisting of n 2-cycles.

The maximal number of partitions of {1..2n} that are invariant under a permutation consisting of n 2-cycles, and which have the same number of nonempty parts.

The number of partitions of {1..3n} that are invariant under a permutation consisting of n 3-cycles.

Sorting numbers (see Motzkin article for details).

Number of weighted linear spaces of total weight n.

Number of connected weighted linear spaces of total weight n.

Bisection of Lucas sequence: a(n) = L(2*n+1).

Number of ways of getting a straight flush, 4 of a kind, full house, flush, straight, 3 of a kind, 2 pair, a pair, nothing in a 7-card poker hand.

Number of 3-connected nets with n edges.

Number of simple imperfect squared rectangles of order n up to symmetry.

Nearest integer to Bernoulli number B_{2n}.

Number of allomorphic polyhedra with n nodes.

Number of nonsingular n X n matrices over GF(2) (order of the group GL(n,2)); order of Chevalley group A_n (2); order of projective special linear group PSL_n(2).

Number of cyclic Steiner triple systems of order 2n+1.

Van der Waerden numbers W(2;2,n-1).

The minimum number of nodes of a tree with a cutting center of n nodes.

a(n) is the cutting number of the tree corresponding to A002887(n).

Arrays of dumbbells.

Low temperature series for spin-1/2 Ising partition function on 2D square lattice.

Low temperature series for spin-1/2 Ising partition function on 3-dimensional simple cubic lattice.

Low-temperature series for partition function for spin-1/2 Ising model on f.c.c. lattice.

a(n) = Sum_{k=0..n} binomial(n,k)^2 * binomial(2*k,k).

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

Domb numbers: number of 2n-step polygons on diamond lattice.

Number of 2n-step polygons on cubic lattice.

a(n) = binomial(2n,n)^3.

Number of n-step closed paths on hexagonal lattice.

Number of n-step polygons on f.c.c. lattice.

Number of n-step walks on square lattice.

a(n) = n^3 - floor( n/3 ).

Number of n-step self-avoiding walks on a cubic lattice with a first step along the positive x, y, or z axis.

Number of n-step self-avoiding walks on b.c.c. lattice (version 1).

Delete all letters except c, d, i, l, m, v, x from the US English name of n, then read as Roman numeral if possible, otherwise 0.

Number of connected graphs with n edges.

High temperature series for spin-1/2 Ising magnetic susceptibility on 2D square lattice.

High temperature series in v = tanh(J/kT) for residual correlation function (correction to susceptibility) for the spin-1/2 Ising model on square lattice.

High temperature expansion of -u/J in odd powers of v = tanh(J/kT), where u is energy per site of the spin-1/2 Ising model on square lattice with nearest-neighbor interaction J at temperature T.

Low temperature energy function for square lattice.