OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..450
FORMULA
G.f.: exp(Sum_{k>=1} ( Sum_{d|k} (-1)^(k/d+1)*d*((d - 1)!)^(k/d) ) * x^k/k).
a(n) ~ (n-1)! * (1 + 1/n + 2/n^2 + 7/n^3 + 34/n^4 + 203/n^5 + 1454/n^6 + 12321/n^7 + 121326/n^8 + 1364947/n^9 + 17301550/n^10 + ...). - Vaclav Kotesovec, Nov 13 2018
MAPLE
b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, 1, b(n, i-1)+b(n-i, min(n-i, i-1))*(i-1)!))
end:
a:= n-> b(n$2):
seq(a(n), n=0..24); # Alois P. Heinz, Jul 05 2023
MATHEMATICA
nmax = 22; CoefficientList[Series[Product[(1 + (k - 1)! x^k), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) d ((d - 1)!)^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 22}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 12 2018
STATUS
approved