A258325 a(n) = Product_{k=1..n} (1 + p(k)), where p(k) is the partition function A000041.

1, 2, 6, 24, 144, 1152, 13824, 221184, 5087232, 157704192, 6781280256, 386532974592, 30149572018176, 3075256345853952, 418234863036137472, 74027570757396332544, 17174396415715949150208, 5117970131883352846761984, 1975536470906974198850125824

Offset: 0

Author

Vaclav Kotesovec, Jul 19 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150
• Vaclav Kotesovec, The partition factorial constant and asymptotics of the sequence A058694

Crossrefs

Cf. A000041, A058694, A078506, A082480.

Programs

Maple

a:= proc(n) option remember: `if`(n<1, 1,
      (1+combinat[numbpart](n))*a(n-1))
    end:
seq(a(n), n=0..20);

Mathematica

Table[Product[PartitionsP[k]+1,{k,1,n}],{n,0,20}]

Formula

a(n) ~ c * A058694(n), where c = Product_{k>=1} (1 + 1/p(k)) = 7.60150293364724365227288154074110141857580676049277152624021470033199348...

Extensions

a(0)=1 prepended by Alois P. Heinz, Jul 26 2015