A292386 Expansion of Product_{k>=1} (1 - x^k)^(k*(k+1)/2).

1, -1, -3, -3, -1, 10, 20, 36, 28, -11, -103, -245, -397, -448, -214, 464, 1817, 3680, 5660, 6473, 4362, -3232, -18428, -41946, -70589, -94890, -96996, -49673, 78907, 317995, 673299, 1105044, 1491333, 1605102, 1094914, -479358, -3561322, -8404118, -14781724, -21595744, -26450603, -25329527

Offset: 0

Author

Ilya Gutkovskiy, Sep 15 2017

Keywords

• sign

Comments

Convolution inverse of A000294 (Euler transform of the triangular numbers).

Crossrefs

Cf. A000294, A027999, A028377.

Programs

Mathematica

nmax = 41; CoefficientList[Series[Product[(1 - x^k)^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x]

SageMath

# uses[EulerTransform from A166861]
b = EulerTransform(lambda n: -binomial(n+1, 2))
print([b(n) for n in range(37)]) # Peter Luschny, Nov 11 2020

Formula

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