A296237 - OEIS

%I #14 Mar 06 2020 06:48:09

%S 1,0,1,0,1,0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,4,3,5,4,6,4,6,5,

%T 6,6,7,7,7,7,9,8,10,9,11,10,11,12,12,13,13,14,15,14,17,16,19,18,20,20,

%U 21,22,23,24,25,25,28,27,30,29,33,32,35,35,37,38,39

%N Expansion of Product_{k>0} 1/(1 - x^(k*(3*k+1)/2)).

%C Integer partitions into second or "negative" pentagonal numbers (A005449) .

%H Seiichi Manyama, <a href="/A296237/b296237.txt">Table of n, a(n) for n = 0..10000</a>

%t nmax = 100; CoefficientList[Series[Product[1/(1 - x^(k*(3*k+1)/2)), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Dec 10 2017 *)

%o (PARI) N=66; x='x+O('x^N); Vec(1/prod(k=1, N, (1-x^(k*(3*k+1)/2))))

%Y Cf. A005449, A095699, A218379, A296238.

%K nonn

%O 0,15

%A _Seiichi Manyama_, Dec 09 2017