Sequences

a(n) = largest integer m such that every n-point interval order contains an m-point semiorder.

Number of non-vanishing Feynman diagrams of order 2n for the electron or the photon propagators in quantum electrodynamics.

Number of non-vanishing Feynman diagrams of order 2n for the vacuum polarization (the proper two-point function of the photon) and for the self-energy (the proper two-point function of the electron) in quantum electrodynamics (QED).

Number of non-vanishing Feynman diagrams of order 2n+1 for the electron-electron-photon proper vertex function in quantum electrodynamics (QED).

Feynman diagrams of order 2n with vertex skeletons.

Number of simple tensors with n external gluons.

Vertex diagrams of order 2n.

Maximal period of an n-stage shift register.

Number of (n-1)-bead black-white reversible strings; also binary grids; also row sums of Losanitsch's triangle A034851; also number of caterpillar graphs on n+2 vertices.

Number of nonequivalent dissections of a polygon into n heptagons by nonintersecting diagonals up to rotation and reflection.

Largest prime factor of 2^n - 1.

Number of numbers of complexity n, i.e., that can be built from n ones using + and *, and require at least that many ones.

Largest prime factor of 10^n - 1.

A finite sequence associated with the Lie algebra A_6.

Smallest number that requires n iterations of the bi-unitary totient function (A116550) to reach 1.

a(n) = 2*a(n-1) + (n-1)*a(n-2).

Number of linear geometries on n points with <= 3 points per line.

Josephus problem: numbers m such that, when m people are arranged on a circle and numbered 1 through m, the final survivor when we remove every 4th person is one of the first three people.

a(n) = ceiling((1 + sum of preceding terms) / 2) starting with a(0) = 1.

Apéry numbers: n^3*C(2n,n).

Apéry numbers: n*C(2*n,n).

Embeddings of n-bouquet in sphere.

Number of permutation groups of degree n (or, number of distinct subgroups of symmetric group S_n, counting conjugates as distinct).

A finite sequence associated with the Lie algebra B_3.

Number of distinct autocorrelations of binary words of length n.

Number of column-convex polyominoes with perimeter 2n+2.

Number of convex polygons of perimeter 2n on square lattice.

Column of Kempner tableau.

Column of Kempner tableau.

Genocchi medians (or Genocchi numbers of second kind).

Coefficients of Gandhi polynomials.

Number of isonemal fabrics of period exactly n.

a(n) = n!*Fibonacci(n+1).

a(n) = n! * Fibonacci(n).

From a Fibonacci-like differential equation.

From a Fibonacci-like differential equation.

Denominators of expansion of -W_{-1}(-e^{-1-x^2/2}) where W_{-1} is Lambert W function.

Numerators of the expansion of -W_{-1}(-e^(-1 - x^2/2)) where x > 0 and W_{-1} is the Lambert W function.

Centered triangular numbers: a(n) = 3*n*(n-1)/2 + 1.

Second pentagonal numbers: a(n) = n*(3*n + 1)/2.

Numerator of (1 + Gamma(n))/n.

a(n) = 1 if n is a prime number, otherwise a(n) = n.

Number of positions that the 3 X 3 X 3 Rubik cube puzzle can be in after exactly n moves, up to equivalence under the full group of order 48 of the cube and with a half-turn is considered to be 2 moves.

A finite sequence associated with the Lie algebra B_4.

A finite sequence associated with the Lie algebra C_3.

A finite sequence associated with the Lie algebra C_4.

A finite sequence associated with the Lie algebra D_4.

A finite sequence associated with the Lie algebra D_5.

A finite sequence associated with the Lie algebra F_4.

A finite sequence associated with the Lie algebra E_6.