OFFSET
0,4
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..400
FORMULA
G.f.: Sum_{k>=0} !k * x^k / Product_{j=1..k} (1 - x^j).
a(n) ~ exp(-1) * n! * (1 + 1/n + 2/n^2 + 5/n^3 + 16/n^4 + 60/n^5 + 253/n^6 + 1180/n^7 + 6023/n^8 + 33306/n^9 + 197719/n^10 + ...), for coefficients see A331826. - Vaclav Kotesovec, Jan 28 2020
MATHEMATICA
Table[Sum[Length[IntegerPartitions[n, {k}]] Subfactorial[k], {k, 0, n}], {n, 0, 22}]
nmax = 22; CoefficientList[Series[Sum[Subfactorial[k] x^k/Product[(1 - x^j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 19 2020
STATUS
approved