A292387 Expansion of Product_{k>=1} (1 - x^k)^(k*(k+1)*(k+2)/6).

1, -1, -4, -6, -4, 19, 60, 131, 149, -4, -572, -1764, -3485, -4716, -2658, 7606, 32944, 77152, 132586, 161275, 75150, -281687, -1111029, -2560293, -4470415, -5922117, -4603551, 3799070, 25573251, 67259095, 130430051, 201158707, 232853019, 124749892, -295134275, -1260897993, -2995361708, -5515840117

Offset: 0

Author

Ilya Gutkovskiy, Sep 15 2017

Keywords

• sign

Comments

Convolution inverse of A000335 (Euler transform of the tetrahedral numbers).

Crossrefs

Cf. A000335, A258343, A292386.

Programs

Mathematica

nmax = 37; CoefficientList[Series[Product[(1 - x^k)^(k (k + 1) (k + 2)/6), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} (1 - x^k)^(k*(k+1)*(k+2)/6).