A244519 Expansion of Product_{n>=1} (1 + H(x^n)) where H(x) is the g.f. of A000081.

1, 1, 2, 4, 8, 16, 35, 76, 175, 414, 1009, 2510, 6382, 16448, 42961, 113352, 301715, 808932, 2182739, 5921803, 16143975, 44199809, 121477237, 335015538, 926814691, 2571322157, 7152404733, 19942874638, 55729271645, 156051344975, 437801148097, 1230423785329, 3463777894236, 9766002585763, 27574869734583, 77965430442158

Offset: 0

Author

Joerg Arndt, Jul 10 2014

Keywords

• nonn

Comments

Which combinatorial objects does this sequence count?

Links

• Joerg Arndt, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A001372 (expansion of 1/Product_{n>=1} (1 - H(x^n))).

Programs

PARI

N=66;  A=vector(N+1, j, 1);
for (n=1, N, A[n+1] = 1/n * sum(k=1, n, sumdiv(k, d, d * A[d]) * A[n-k+1] ) );
A000081=concat([0], A);
H(t)=subst(Ser(A000081, 't), 't, t);
x='x+O('x^N);
T=prod(n=1,N, 1 + H(x^n));
Vec(T)