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

Author

Ilya Gutkovskiy, Oct 29 2018

Keywords

• nonn

Links

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

Crossrefs

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

Programs

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 *)

Formula

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