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%I #31 Jul 26 2015 09:56:55
%S 1,2,6,24,144,1152,13824,221184,5087232,157704192,6781280256,
%T 386532974592,30149572018176,3075256345853952,418234863036137472,
%U 74027570757396332544,17174396415715949150208,5117970131883352846761984,1975536470906974198850125824
%N a(n) = Product_{k=1..n} (1 + p(k)), where p(k) is the partition function A000041.
%H Alois P. Heinz, <a href="/A258325/b258325.txt">Table of n, a(n) for n = 0..150</a>
%H Vaclav Kotesovec, <a href="http://oeis.org/A058694/a058694_2.pdf">The partition factorial constant and asymptotics of the sequence A058694</a>
%F a(n) ~ c * A058694(n), where c = Product_{k>=1} (1 + 1/p(k)) = 7.60150293364724365227288154074110141857580676049277152624021470033199348...
%p a:= proc(n) option remember: `if`(n<1, 1,
%p (1+combinat[numbpart](n))*a(n-1))
%p end:
%p seq(a(n), n=0..20);
%t Table[Product[PartitionsP[k]+1,{k,1,n}],{n,0,20}]
%Y Cf. A000041, A058694, A078506, A082480.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jul 19 2015
%E a(0)=1 prepended by _Alois P. Heinz_, Jul 26 2015
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