A058892 E.g.f.: exp(f(x)-1), where f(x) = o.g.f. for partitions (A000041), Product_{k>=1} 1/(1-x^k).

1, 1, 5, 31, 265, 2621, 31621, 426595, 6574961, 111673945, 2092318021, 42552808871, 937495160185, 22150499622421, 559765402811525, 15039597200385451, 428293292251548001, 12875707199330296625, 407547173842501629061

Offset: 0

Author

N. J. A. Sloane, Jan 08 2001

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..422

Crossrefs

Cf. A000041, A038048.

Programs

Mathematica

nmax = 30; CoefficientList[Series[1/E*Exp[Product[1/(1 - x^k), {k, 1, nmax}]], {x, 0, nmax}], x] * Range[0, nmax]!(* Vaclav Kotesovec, Aug 19 2015 *)

PARI

N=66; q='q+O('q^N);
f=exp( 1/prod(n=1,N, 1-q^n ) - 1 );
egf=serlaplace(f);
Vec(egf)
/* Joerg Arndt, Oct 06 2012 */

Formula

a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} k*A000041(k)*a(n-k)/(n-k)! for n > 0. - Seiichi Manyama, Oct 15 2017