A307128 Expansion of Product_{j>=1} (1 + (-1 + Product_{k>=1} (1 + x^k))^j).

1, 1, 2, 6, 15, 40, 103, 266, 683, 1753, 4481, 11417, 28993, 73414, 185424, 467302, 1175322, 2950467, 7393090, 18492029, 46173538, 115102596, 286482967, 711990108, 1767048214, 4379814978, 10842382074, 26808912074, 66212421302, 163351562975, 402575169429, 991119918949

Offset

0,3

Links

Table of n, a(n) for n=0..31.

Formula

G.f.: q(q(x) - 1), where q(x) = g.f. of A000009 (number of partitions into distinct parts).

Mathematica

nmax = 31; CoefficientList[Series[Product[(1 + (-1 + Product[(1 + x^k), {k, 1, nmax}])^j), {j, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000009, A307127.

Sequence in context: A321646 A246563 A259399 * A172399 A001654 A062106

Adjacent sequences: A307125 A307126 A307127 * A307129 A307130 A307131

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 26 2019

Status

approved