A307438 - OEIS

A307438

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

1, 1, 0, 2, 0, 5, 1, 9, 2, 17, 10, 26, 39, 22, 136, -69, 450, -474, 1457, -1920, 4543, -6596, 13627, -20780, 39356, -61431, 109448, -171688, 292114, -453814, 741646, -1126365, 1760851, -2566719, 3762671, -5049452, 6482765, -6806770, 4649834, 5114037, -30577380

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..40.

FORMULA

G.f.: g(g(x) - 1), where g(x) = g.f. of A081362.

MATHEMATICA

nmax = 40; CoefficientList[Series[Product[1/(1 + (-1 + Product[1/(1 + x^k), {k, 1, nmax}])^j), {j, 1, nmax}], {x, 0, nmax}], x]

nmax = 40; CoefficientList[Series[QPochhammer[QPochhammer[x, x^2] - 1, (QPochhammer[x, x^2] - 1)^2], {x, 0, nmax}], x]

CROSSREFS

Cf. A081362, A306456, A307127, A307128.