A316788 Expansion of Product_{k>=1} (1 - x^(k*(k+1)/2)) / (1 + x^(k*(k+1)/2)).

1, -2, 2, -4, 6, -6, 6, -6, 6, -4, 0, 2, -2, 6, -10, 6, -2, 2, 2, -10, 16, -18, 18, -22, 26, -18, 10, -12, 4, 10, -14, 18, -22, 24, -26, 18, -8, 6, 6, -24, 28, -34, 44, -38, 30, -28, 14, 2, -10, 22, -28, 36, -50, 38, -30, 44, -28, 0, 2, -10, 34, -54, 66, -66, 70, -82, 60

Offset: 0

Author

Seiichi Manyama, Jul 13 2018

Keywords

• sign

Comments

For n <= 10^4, a(n) = 0 for n = 10, 57, 78, 136, 141.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A280366, A292518, A292519.

Programs

Maple

seq(coeff(series(mul((1-x^(k*(k+1)/2))/(1+x^(k*(k+1)/2)),k=1..n), x,n+1),x,n),n=0..70); # Muniru A Asiru, Jul 14 2018

Mathematica

nmax = 100; CoefficientList[Series[Product[(1 - x^(k*(k+1)/2)) / (1 + x^(k*(k+1)/2)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 14 2018 *)

Formula

Convolution inverse of A280366.