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

%I A058892 #15 Oct 15 2017 12:47:45
%S A058892 1,1,5,31,265,2621,31621,426595,6574961,111673945,2092318021,
%T A058892 42552808871,937495160185,22150499622421,559765402811525,
%U A058892 15039597200385451,428293292251548001,12875707199330296625,407547173842501629061
%N A058892 E.g.f.: exp(f(x)-1), where f(x) = o.g.f. for partitions (A000041), Product_{k>=1} 1/(1-x^k).
%H A058892 Seiichi Manyama, <a href="/A058892/b058892.txt">Table of n, a(n) for n = 0..422</a>
%F A058892 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
%t A058892 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 *)
%o A058892 (PARI)
%o A058892 N=66; q='q+O('q^N);
%o A058892 f=exp( 1/prod(n=1,N, 1-q^n ) - 1 );
%o A058892 egf=serlaplace(f);
%o A058892 Vec(egf)
%o A058892 /* _Joerg Arndt_, Oct 06 2012 */
%Y A058892 Cf. A000041, A038048.
%K A058892 nonn
%O A058892 0,3
%A A058892 _N. J. A. Sloane_, Jan 08 2001