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%I #19 Sep 17 2017 23:16:20
%S 1,0,0,0,0,0,2,2,4,0,2,4,4,0,30,46,78,0,210,366,644,0,2032,3696,6694,
%T 0,21936,39886,73098,0,246172,454074,841714,0,2899542,5401222,
%U 10073398,0,35282910,66213604,124427582,0,441326270,832775792,1573861942,0,5642205488
%N Number of solutions to +-1 +- 5 +- 12 +- ... +- n*(3*n-1)/2 = 0.
%H Seiichi Manyama, <a href="/A292474/b292474.txt">Table of n, a(n) for n = 0..200</a>
%F Constant term in the expansion of Product_{k=1..n} (x^(k*(3*k-1)/2)+1/x^(k*(3*k-1)/2)).
%F a(4*k+1) = 0 for k >= 0.
%e For n=6 the 2 solutions are +1+5-12+22+35-51 = 0 and -1-5+12-22-35+51 = 0.
%o (PARI) {a(n) = polcoeff(prod(k=1, n, x^(k*(3*k-1)/2)+1/x^(k*(3*k-1)/2)), 0)}
%Y Cf. A000326, A002411, A158092, A158380, A292475.
%K nonn
%O 0,7
%A _Seiichi Manyama_, Sep 17 2017