Sequences

Number of connected labeled 2-regular oriented graphs with n nodes.

Number of unlabeled graphs with n nodes and degree >= 3.

Number of connected unlabeled graphs with n nodes and degree >= 3.

Expansion of e.g.f. (1 + x)^x.

Expansion of e.g.f. (1 - x)^x.

Expansion of e.g.f. (1 - x - x^2)^x.

Expansion of e.g.f. (1+x)^(exp(x)).

a(0) = a(1) = 0; for n >= 2, a(n)*2^(n+2) + 1 is the smallest prime factor of the n-th Fermat number F(n) = 2^(2^n) + 1.

Expansion of e.g.f. (1+x)^sin(x).

Expansion of (1-x)^sin(x).

Expansion of e.g.f. (1+x)^(1-x).

Expansion of e.g.f. ( (1+x)^x )^x.

Number of unlabeled identity connected unit interval graphs with n nodes.

Number of connected unit interval graphs with n nodes; also number of bracelets (turnover necklaces) with n black beads and n-1 white beads.

Number of strength 1 Eulerian graphs with n nodes, 2 of odd degree.

Number of connected strength-1 Eulerian graphs with n nodes, 2 of odd degree.

Number of connected rooted strength 1 Eulerian graphs with n nodes.

Definition (1): Number of unlabeled strength-2 Eulerian graphs with n nodes.

Number of unlabeled strength 3 Eulerian graphs with n nodes.

Number of unlabeled strength 3 Eulerian graphs with n nodes, 2 of odd degree.

Number of unlabeled rooted strength 3 Eulerian graphs with n nodes.

Number of unlabeled connected strength 3 Eulerian graphs with n nodes.

Number of unlabeled connected strength 3 Eulerian graphs with n nodes, 2 of odd degree.

Number of unlabeled rooted connected strength 3 Eulerian graphs with n nodes.

Number of connected labeled chordal graphs (or triangulated graphs) with n nodes.

Number of symmetry sites in all planted 1,3-trees with 2n nodes.

Number of symmetry sites in all planted 3-trees with n nodes.

Number of rooted maps with n edges on the projective plane.

Smallest primitive factor of 10^n - 1. Also smallest prime p such that 1/p has repeating decimal expansion of period n.

Number of unlabeled bicolored bipartite graphs on 2n nodes having n nodes of each color with no edges between vertices of the same color and allowing the color classes to be interchanged.

Number of unlabeled bicolored graphs, with no isolated nodes, on 2n nodes having n nodes of each color and allowing the color classes to be interchanged.

E-trees with at most 2 colors.

E-trees with at most 3 colors.

E-trees with exactly 2 colors.

E-trees with exactly 3 colors.

Number of rooted bridgeless graphs with n nodes.

Number of unlabeled simple connected bridgeless graphs with n nodes.

Number of self-dual 2-colored necklaces with 2n beads.

Number of self-complementary 2-colored bracelets (turnover necklaces) with 2n beads.

2-part of number of graphs on n nodes.

2-part of number of tournaments on n nodes.

Number of planted evolutionary trees of magnitude n.

Evolutionary trees of magnitude n.

Dedekind numbers: number of monotone Boolean functions or antichains of subsets of an n-set containing at least one nonempty set.

Spectrum of the free Kleene algebra on n free variables.

(2^(2^n))*(3^(3^n - 2^n)).

Spectrum of a certain 3-element algebra.

Essentially n-ary operations in Kleene free algebra.

Essentially n-ary operations in a certain 3-element algebra.

Essentially n-ary operations in a certain 3-element algebra.