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%I #15 Jan 28 2022 17:11:39
%S 1,1,0,0,2,3,0,0,12,21,0,0,113,202,0,0,1218,2241,0,0,14326,26776,0,0,
%T 177714,335607,0,0,2287975,4353975,0,0,30282850,57965473,0,0,
%U 409476546,787414730,0,0,5631955466,10870618388,0,0,78545902971,152074824054,0,0
%N Number of solutions to +- 1 +- 2 +- 3 +- ... +- n = n.
%H Ray Chandler, <a href="/A063890/b063890.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = [x^n] Product_{k=1..n} (x^k + 1/x^k). - _Ilya Gutkovskiy_, Jan 28 2022
%e a(8) = 12 because 8 = 1+2+3+4+5-6+7-8 = -1+2+3+4-5+6+7-8 = 1-2+3-4+5+6+7-8 = -1-2-3+4+5+6+7-8 = -1+2+3+4+5-6-7+8 = 1-2+3+4-5+6-7+8 = 1+2-3-4+5+6-7+8 = -1-2+3-4+5+6-7+8 = 1+2-3+4-5-6+7+8 = -1-2+3+4-5-6+7+8 = -1+2-3-4+5-6+7+8 = 1-2-3-4-5+6+7+8.
%t f[n_, s_] := f[n, s]=Which[n==0, If[s==0, 1, 0], Abs[s]>(n*(n+1))/2, 0, True, f[n-1, s-n]+f[n-1, s+n]]; a[n_] := f[n, n]
%t nmax = 44; d = {1}; a1 = {1};
%t Do[
%t d = PadLeft[d, Length[d] + 2 n] + PadRight[d, Length[d] + 2 n];
%t i = Ceiling[Length[d]/2] + n;
%t AppendTo[a1, If[i > Length[d], 0, d[[i]]]];
%t , {n, nmax}];
%t a1 (* _Ray Chandler_, Mar 25 2014 *)
%Y Cf. A025591, A063865-A063867.
%K nonn
%O 0,5
%A _Vladeta Jovovic_, Aug 28 2001
%E More terms from _Dean Hickerson_, Aug 30, 2001
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