OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..443
FORMULA
a(n) ~ exp(1) * n! * A000009(n).
a(n) ~ sqrt(2*Pi) * exp(Pi*sqrt(n/3) - n + 1) * n^(n - 1/4) / (4*3^(1/4)).
E.g.f.: exp(x) * Product_{k>=1} (1 + x^k). - Ilya Gutkovskiy, Oct 15 2018
MATHEMATICA
Table[Sum[Binomial[n, k]*k!*PartitionsQ[k], {k, 0, n}], {n, 0, 20}]
PROG
(PARI) x='x+O('x^30); Vec(serlaplace(exp(x)*eta(x^2)/eta(x))) \\ G. C. Greubel, Oct 15 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(x)*(&*[1 + x^k: k in [1..50]]))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Oct 15 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 31 2017
STATUS
approved