A321192 a(n) = [x^n] Product_{k>=1} (1 + x^k)^tau_n(k), where tau_n(k) = number of ordered n-factorizations of k.

1, 1, 2, 6, 20, 55, 239, 700, 3212, 10104, 48622, 161579, 806843, 2799199, 14379647, 52018828, 273472712, 1023655306, 5491615463, 21234676241, 115910309103, 460998296937, 2556361045845, 10440651927427, 58714921974979, 245586789818255, 1399187406060485

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..500

Formula

a(n) = [x^n] Product_{k_1>=1, k_2>=1, ..., k_n>=1} (1 + x^(k_1*k_2*...*k_n)).

Mathematica

tau[n_, 1] = 1; tau[n_, k_] := tau[n, k] = Plus @@ (tau[#, k-1] & /@ Divisors[n]); nmax = 30; Table[SeriesCoefficient[Product[(1 + x^k)^tau[k, n], {k, 1, n}], {x, 0, n}], {n, 0, nmax}] (* Vaclav Kotesovec, Oct 29 2018 *)

Crossrefs

Cf. A000009, A077592, A107742, A280473, A280486, A321191.

Sequence in context: A347582 A045655 A303307 * A327414 A110295 A027294

Adjacent sequences: A321189 A321190 A321191 * A321193 A321194 A321195

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 29 2018

Status

approved