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

0,3

Comments

Which combinatorial objects does this sequence count?

Links

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

Prog

(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)

Crossrefs

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

Sequence in context: A180207 A013025 A034339 * A247293 A337716 A126137

Adjacent sequences: A244516 A244517 A244518 * A244520 A244521 A244522

Keyword

nonn

Author

Joerg Arndt, Jul 10 2014

Status

approved