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

0,2

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

Formula

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

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}]

Crossrefs

Cf. A000041, A058694, A078506, A082480.

Sequence in context: A356858 A375812 A375808 * A191006 A082471 A275594

Adjacent sequences: A258322 A258323 A258324 * A258326 A258327 A258328

Keyword

nonn

Author

Vaclav Kotesovec, Jul 19 2015

Extensions

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

Status

approved