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Expansion of Sum_{k>=0} (-1)^k * x^(k*(3*k+1)/2) / Product_{j=1..k} (1-x^j).
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%I #14 Jan 17 2022 09:19:01

%S 1,0,-1,-1,-1,-1,-1,0,0,1,1,2,2,3,3,3,3,3,2,2,1,0,-1,-2,-4,-5,-6,-8,

%T -9,-10,-11,-12,-12,-13,-12,-12,-11,-10,-7,-6,-3,0,4,7,12,15,21,25,30,

%U 34,40,43,48,51,55,56,59,59,60,58,56,52,49,42,35,26,17,5,-7,-21,-36,-52,-69,-87,-105,-124,-144,-163

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

%o (PARI) my(N=99, x='x+O('x^N)); Vec(sum(k=0, N, (-1)^k*x^(k*(3*k+1)/2)/prod(j=1, k, 1-x^j)))

%Y Cf. A039924, A237979, A350310, A350738.

%K sign

%O 0,12

%A _Seiichi Manyama_, Jan 12 2022