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%I #20 Mar 10 2023 05:39:19
%S 1,0,2,2,8,20,68,206,692,2306,7930,27492,96792,343670,1231932,4447510,
%T 16164914,59086618,217091832,801247614,2969432270,11045446688,
%U 41224168020,154329373022,579377940390,2180684278698,8227240466520,31107755899600
%N Number of solutions to +-1 +- 3 +- 5 +- 7 +- ... +- (4*n-1) = 0.
%F Constant term in the expansion of Product_{k=1..2*n} (x^(2*k-1)+1/x^(2*k-1)).
%F a(n) = 2*A156700(n) for n > 0.
%e For n=2 the 2 solutions are +1-3-5+7 = 0 and -1+3+5-7 = 0.
%e For n=3 the 2 solutions are +1+3+5-7+9-11 = 0 and -1-3-5+7-9+11 = 0.
%t a[n_] := SeriesCoefficient[Product[x^(2k - 1) + 1/x^(2k - 1), {k, 1, 2n}], {x, 0, 0}];
%t Table[a[n], {n, 0, 27}] (* _Jean-François Alcover_, Mar 10 2023 *)
%o (PARI) {a(n) = polcoeff(prod(k=1, 2*n, x^(2*k-1)+1/x^(2*k-1)), 0)}
%Y Cf. A063865, A156700, A292496.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Sep 17 2017
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