A305355 Expansion of Product_{k>=1} (1 - x^(k*(3*k-1)/2)).

1, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 1, -1, 0, 0, 0, -1, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, -1, 2, -1, 0, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, -1, 0, -1, 1, 0, 0, 1

Offset: 0

Author

Seiichi Manyama, May 31 2018

Keywords

• sign

Links

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

Crossrefs

Product_{k>=1} (1 - x^(k*((m-2)*k-(m-4))/2)): A292518 (m=3), A276516 (m=4), this sequence (m=5).

Cf. A000326, A218379, A218380.

Programs

Maple

seq(coeff(series(mul(1-x^(k*(3*k-1)/2),k=1..n), x,n+1),x,n),n=0..140); # Muniru A Asiru, May 31 2018