A321191 a(n) = [x^n] Product_{k>=1} 1/(1 - x^k)^tau_n(k), where tau_n(k) = number of ordered n-factorizations of k.

1, 1, 3, 7, 29, 71, 336, 932, 4593, 13690, 69708, 222718, 1163734, 3902016, 20825927, 73229397, 397806717, 1452193925, 8016518379, 30328368519, 169781766056, 662143701506, 3755514158949, 15071604241851, 86496856963200, 356063096545571, 2066351471542036

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/(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/(1 - x^k)^tau[k, n], {k, 1, n}], {x, 0, n}], {n, 0, nmax}] (* Vaclav Kotesovec, Oct 29 2018 *)

Crossrefs

Cf. A000041, A006171, A077592, A174465, A280487, A321192.

Sequence in context: A261270 A171134 A080806 * A363666 A148759 A148760

Adjacent sequences: A321188 A321189 A321190 * A321192 A321193 A321194

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 29 2018

Status

approved