A305355 - OEIS

%I #17 Jun 01 2018 06:36:23

%S 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,

%T 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,

%U -1,2,-1,0,0,0,-1,0,0,1,0,1,0,0,-1,0,-1,1,0,0,1

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

%H Seiichi Manyama, <a href="/A305355/b305355.txt">Table of n, a(n) for n = 0..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Pentagonal_number">Pentagonal number</a>

%p 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

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

%Y Cf. A000326, A218379, A218380.

%K sign

%O 0,36

%A _Seiichi Manyama_, May 31 2018