A341505 E.g.f.: Product_{i>=1, j>=1} 1 / (1 - x^(i*j) / (i*j)!).

1, 1, 4, 14, 77, 427, 3076, 23088, 205316, 1936275, 20611750, 233576818, 2909340750, 38527889389, 551372037898, 8364582709282, 135560933977809, 2320127265064403, 42072789623722518, 802547153889643250, 16118882845967168807, 339268639052195731063

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..447

Formula

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

a(n) ~ c * n!, where c = Product_{k>=2} 1/(1 - 1/k!)^sigma_0(k) = 6.6953800201104498115311861820134227776761182601282551253439990653959... - Vaclav Kotesovec, Feb 20 2021

Mathematica

nmax = 21; CoefficientList[Series[Product[1/(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, 21}]

Crossrefs

Cf. A000005, A005651, A006171, A174661, A318693, A340903, A341506, A341876.

Sequence in context: A222900 A222485 A009347 * A231510 A161132 A186638

Adjacent sequences: A341502 A341503 A341504 * A341506 A341507 A341508

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 13 2021

Status

approved