OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..409
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * p(k) * a(n-k).
a(n) ~ c * d^n * n!, where d = 1.769410350604938716841596133605930996231892313627986058432895713767619380283... and c = 0.6329116440270047042622953043644713645679657251851049998748689226219... - Vaclav Kotesovec, Sep 03 2019
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(a(n-k)*
binomial(n, k)*combinat[numbpart](k), k=1..n))
end:
seq(a(n), n=0..20); # Alois P. Heinz, Sep 02 2019
MATHEMATICA
nmax = 20; CoefficientList[Series[1/(1 - Sum[PartitionsP[k] x^k/k!, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] PartitionsP[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 02 2019
STATUS
approved