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A258325
a(n) = Product_{k=1..n} (1 + p(k)), where p(k) is the partition function A000041.
3
1, 2, 6, 24, 144, 1152, 13824, 221184, 5087232, 157704192, 6781280256, 386532974592, 30149572018176, 3075256345853952, 418234863036137472, 74027570757396332544, 17174396415715949150208, 5117970131883352846761984, 1975536470906974198850125824
OFFSET
0,2
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 19 2015
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Jul 26 2015
STATUS
approved