A321287 Expansion of Product_{k>=1} (1 + x^k)^tau_k(k), where tau_k(k) = number of ordered k-factorizations of k (A163767).

1, 1, 2, 5, 14, 22, 70, 109, 318, 551, 1203, 2136, 5752, 9263, 20641, 37151, 85084, 144918, 317356, 546730, 1196302, 2076810, 4281584, 7459351, 15860805, 27146911, 54715933, 95712097, 194059563, 334322338, 663159101, 1147479053, 2270647257, 3923732160, 7587368893

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Mathematica

tau[n_, 1] = 1; tau[n_, k_]:=tau[n, k] = Plus @@ (tau[#, k-1] & /@ Divisors[n]); nmax = 40; CoefficientList[Series[Product[(1+x^k)^tau[k, k], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 03 2018, after Robert G. Wilson v *)

Crossrefs

Cf. A163767, A304965, A321192.

Sequence in context: A176191 A265248 A131661 * A076664 A220477 A049939

Adjacent sequences: A321284 A321285 A321286 * A321288 A321289 A321290

Keyword

nonn

Author

Seiichi Manyama, Nov 02 2018

Status

approved