OFFSET
0,5
MATHEMATICA
nmax = 35; CoefficientList[Series[Product[(1 + x^(k (k + 1)/2)/(k (k + 1)/2)!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, (n - 1)! Sum[DivisorSum[k, -#/(-#!)^(k/#) &, IntegerQ[Sqrt[8 # + 1]] &] a[n - k]/(n - k)!, {k, 1, n}]]; Table[a[n], {n, 0, 35}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 11 2020
STATUS
approved