A307321 Expansion of Product_{j>=1} 1/(1 - (-1 + Product_{k>=1} 1/(1 - x^k)^k)^j)^j.

1, 1, 6, 30, 143, 660, 3000, 13448, 59696, 262788, 1148738, 4989908, 21551733, 92596511, 395921737, 1685304092, 7143861196, 30163965903, 126895681419, 531986033218, 2222961809367, 9260148591001, 38461580964389, 159302487751844, 658054630483936, 2711429650817356

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

G.f.: g(g(x) - 1), where g(x) = g.f. of A000219 (number of planar partitions).

Mathematica

nmax = 25; CoefficientList[Series[Product[1/(1 - (-1 + Product[1/(1 - x^k)^k, {k, 1, nmax}])^j)^j, {j, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000219, A307127, A307323.

Sequence in context: A220830 A199938 A285195 * A026749 A003279 A221397

Adjacent sequences: A307318 A307319 A307320 * A307322 A307323 A307324

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 02 2019

Status

approved