A341506 E.g.f.: Product_{i>=1, j>=1} (1 + x^(i*j) / (i*j)!).

1, 1, 2, 8, 17, 87, 366, 1514, 8770, 45585, 267586, 1612624, 11914416, 73215391, 522906754, 4364545708, 33150679697, 263662491935, 2151338992440, 20815916251604, 178593028936507, 1714283809331191, 15531842607259512, 158682350653110712, 1667852117293837230

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..610

Formula

E.g.f.: Product_{k>=1} (1 + x^k / k!)^sigma_0(k).

Mathematica

nmax = 24; CoefficientList[Series[Product[(1 + x^k/k!)^DivisorSigma[0, k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, -(n - 1)! Sum[Sum[d DivisorSigma[0, d]/(-d!)^(k/d), {d, Divisors[k]}] a[n - k]/(n - k)!, {k, 1, n}]]; Table[a[n], {n, 0, 24}]

Crossrefs

Cf. A000005, A007837, A032315, A107742, A318694, A340903, A341505, A341876.

Sequence in context: A295147 A215933 A328742 * A154349 A268068 A073601

Adjacent sequences: A341503 A341504 A341505 * A341507 A341508 A341509

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 13 2021

Status

approved