A299105 Expansion of 1/(1 - x*Product_{k>=1} (1 - x^k)).

1, 1, 0, -2, -3, -1, 5, 10, 7, -9, -29, -30, 10, 77, 108, 22, -184, -351, -207, 372, 1041, 969, -516, -2835, -3655, -284, 6990, 12190, 5977, -14957, -37044, -30994, 24144, 103374, 122409, -7715, -262704, -420585, -162274, 589068, 1309674, 972747, -1057935, -3742955

Offset: 0

Author

Ilya Gutkovskiy, Feb 02 2018

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..5000
• N. J. A. Sloane, Transforms

Crossrefs

Antidiagonal sums of A286354.

Cf. similar sequences: A067687, A299106, A299208, A302017, A318581, A318582, A331484.

Cf. A010815, A299108.

Programs

Mathematica

nmax = 43; CoefficientList[Series[1/(1 - x Product[1 - x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
nmax = 43; CoefficientList[Series[1/(1 - x QPochhammer[x, x]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - x*Product_{k>=1} (1 - x^k)).

a(0) = 1; a(n) = Sum_{k=1..n} A010815(k-1)*a(n-k).