A334385 E.g.f.: Product_{k>=1} (1 + x^(k*(k + 1)/2) / (k*(k + 1)/2)!).

1, 1, 0, 1, 4, 0, 1, 7, 0, 84, 841, 11, 0, 286, 4004, 1, 8024, 136136, 816, 7775256, 155195040, 54265, 1193830, 0, 109832360, 2749077760, 84987760, 296010, 10716746041, 310545275069, 1201800600, 2444026056820, 77016647623040, 0, 14402113079955304, 504073957798435640

Offset

0,5

Links

Table of n, a(n) for n=0..35.

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

Cf. A007837, A032310, A053614 (positions of 0's), A115278, A205799.

Sequence in context: A097898 A154884 A338813 * A201560 A255644 A355174

Adjacent sequences: A334382 A334383 A334384 * A334386 A334387 A334388

Keyword

nonn

Author

Ilya Gutkovskiy, May 11 2020

Status

approved