Sequences

Expansion of (1+x)(1+x^2)/(1-x-x^3).

Losing initial positions in game: two players alternate in removing >= 1 stones; last player wins; first player may not remove all stones; each move <= 3 times previous move.

From a nim-like game.

From a nim-like game.

a(n) = floor( Bernoulli(2*n)/(-4*n) ).

a(n) = n' = arithmetic derivative of n: a(0) = a(1) = 0, a(prime) = 1, a(m*n) = m*a(n) + n*a(m).

Sociable numbers: smallest member of each cycle (conjectured).

Continued fraction for e.

Least common multiple (or LCM) of {1, 2, ..., n} for n >= 1, a(0) = 1.

Values of m in the discriminant D = 4*m leading to a new minimum of the L-function of the Dirichlet series L(1) = Sum_{k>0} Kronecker(D,k)/k.

Values of m in the discriminant D = -4*m leading to a new maximum of the L-function of the Dirichlet series L(1) = Sum_{k=1..oo} Kronecker(D,k)/k.

Nonsquare values of m in the discriminant D = 4*m leading to a new maximum of the L-function of the Dirichlet series L(1) = Sum_{k>0} Kronecker(D,k)/k.

Left factorials: !n = Sum_{k=0..n-1} k!.

a(n) = a(n-1)^2 - 2, with a(0) = 6.

Primes of form (p^x - 1)/(p^y - 1), p prime.

n! times number of posets with n elements.

Number of stable trees with n nodes.

Number of trees by stability index.

Number of trees by stability index.

Number of trees with stability index n.

Number of unlabeled series-parallel posets (i.e., generated by unions and sums) with n nodes.

Number of isomorphism classes of connected irreducible posets with n labeled points.

Hadamard maximal determinant problem: largest determinant of a (real) {0,1}-matrix of order n.

Hadamard maximal determinant problem: largest determinant of (+1,-1)-matrix of order n.

Number of iterations of phi(x) at n needed to reach 1.

Number of directed Hamiltonian circuits on n-octahedron with a marked starting node.

Number of inequivalent labeled Hamiltonian circuits on n-octahedron. Interlacing chords joining 2n points on circle.

Number of unlabeled Hamiltonian circuits on n-octahedron (cross polytope); also number of circular chord diagrams with n chords, modulo symmetries.

Number of 5 X 5 matrices with nonnegative integer entries and row and column sums equal to n.

Number of 6 X 6 stochastic matrices of integers: all rows and columns sum to n.

Number of binary vectors with restricted repetitions.

Number of nonequivalent dissections of a polygon into n triangles by nonintersecting diagonals rooted at a cell up to rotation.

Number of nonequivalent dissections of an n-gon into (n-3) polygons by nonintersecting diagonals rooted at a cell up to rotation.

Number of nonequivalent dissections of an n-gon into n-4 polygons by nonintersecting diagonals rooted at a cell up to rotation.

Number of dissections of a polygon.

Number of nonequivalent dissections of an n-gon into n-4 polygons by nonintersecting diagonals up to rotation.

Number of nonequivalent dissections of a polygon into n triangles by nonintersecting diagonals rooted at a cell up to rotation and reflection.

Number of nonequivalent dissections of an n-gon into n-3 polygons by nonintersecting diagonals rooted at a cell up to rotation and reflection.

Number of nonequivalent dissections of an n-gon into n-4 polygons by nonintersecting diagonals rooted at a cell up to rotation and reflection.

Number of nonequivalent dissections of an n-gon into n-3 polygons by nonintersecting diagonals up to rotation and reflection.

Number of nonequivalent dissections of an n-gon into n-4 polygons by nonintersecting diagonals up to rotation and reflection.

Number of nonequivalent dissections of an n-gon into 3 polygons by nonintersecting diagonals up to rotation.

Number of nonequivalent dissections of an n-gon into 3 polygons by nonintersecting diagonals rooted at a cell up to rotation and reflection.

Number of nonequivalent dissections of an n-gon into 3 polygons by nonintersecting diagonals up to rotation and reflection.

Number of nonequivalent dissections of an n-gon by nonintersecting diagonals rooted at a cell up to rotation.

Number of nonequivalent dissections of an n-gon by nonintersecting diagonals up to rotation.

Number of nonequivalent dissections of an n-gon by nonintersecting diagonals rooted at a cell up to rotation and reflection.

a(n) = ceiling(Bernoulli(2n)/(-4n)).

Erdős-Selfridge function: a(n) is the least number m > n+1 such that the least prime factor of binomial(m, n) is > n.

Absolute primes (or permutable primes): every permutation of the digits is a prime.