Sequences

Expansion of e.g.f. cos(tan(x)) (even powers only).

Expansion of e.g.f. cos(tanh(x)) (even powers only).

Expansion of e.g.f. sin(sin(x)) (odd powers only).

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

Fibbinary numbers: if n = F(i1) + F(i2) + ... + F(ik) is the Zeckendorf representation of n (i.e., write n in Fibonacci number system) then a(n) = 2^(i1 - 2) + 2^(i2 - 2) + ... + 2^(ik - 2). Also numbers whose binary representation contains no two adjacent 1's.

Expansion of e.g.f. sin(sin(sin(x))) (odd powers only).

Expansion of e.g.f. tan(sinh(x)) (odd powers only).

Expansion of e.g.f. sin(tanh(x)) (odd powers only).

E.g.f. tan(tan(x)), zeros omitted.

Expansion of tan(x)*cosh(x).

Expansion of e.g.f. tan(tan(tan(x))).

Expansion of e.g.f. tan(tanh(x)) (odd powers only).

E.g.f. sin(sinh(x)) (odd powers only).

E.g.f. exp(tanh(x)).

Number of partitions of n-set into odd blocks.

Expansion of e.g.f. exp( x * exp(-x) ).

Numbers with no 3 adjacent 1's in binary expansion.

Expansion of e.g.f. exp(x * cosh(x)).

Expansion of e.g.f. log(1+x*cos(x)).

Number of perfect matchings (or domino tilings) in graph C_{5} X P_{2n}.

Number of 2-factors in C_5 X P_n.

Number of Hamiltonian cycles in C_5 X P_n.

Number of Hamiltonian paths in C_5 X P_n.

Number of spanning trees in C_5 X P_n.

Number of spanning trees with degrees 1 and 3 in C_5 X P_2n.

Number of perfect matchings (or domino tilings) in W_5 X P_2n.

Number of 2-factors in W_5 X P_n.

Number of Hamiltonian cycles in W_5 X P_n.

Number of Hamiltonian paths in W_5 X P_n.

Number of spanning trees in W_5 X P_n.

Number of spanning trees with degrees 1 and 3 in W_5 X P_2n.

Number of perfect matchings (or domino tilings) in O_5 X P_2n.

Number of 2-factors in O_5 X P_n.

Number of Hamiltonian cycles in O_5 X P_n.

Number of Hamiltonian paths in O_5 X P_n.

Number of spanning trees in (K_5 - e) X P_n.

Number of spanning trees with degrees 1 and 3 in O_5 X P_2n.

Number of perfect matchings (or domino tilings) in K_5 X P_2n.

Number of 2-factors in K_5 X P_n.

Number of Hamiltonian cycles in K_5 X P_n.

Number of Hamiltonian paths in K_5 X P_n.

Number of spanning trees in K_5 x P_n.

Number of Hamiltonian paths in C_4 X P_n.

Number of spanning trees in C_4 X P_n.

Numbers with no adjacent 0's in binary expansion.

Number of spanning trees in S_4 X P_n.

Number of spanning trees with degrees 1 and 3 in S_4 X P_{2n-1}.

Number of perfect matchings (or domino tilings) in D_4 X P_(n-1).

Number of 2-factors in D_4 X P_n.

Number of Hamiltonian cycles in D_4 X P_n.