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%I #27 Jan 07 2021 10:33:22
%S 1,0,0,62,332,0,0,80006,531524,0,0,173607568,1226700784,0,0,
%T 455805857978,3321800235936,0,0,1325490660318216,9841000101286172,0,0,
%U 4108826483323392880,30886378286619335592,0,0,13306426381421174346512,100916492010297213463566
%N a(n) is the constant term in expansion of Product_{ k = 1..n } (x^k + 1/x^k)^3.
%C From _Robert Israel_, Nov 09 2017: (Start)
%C a(n) is the coefficient of x^(3*n*(n+1)/2) in Product_{k=0..n} (x^(2*k)+1)^3.
%C a(n) = 0 if n == 1 or 2 (mod 4). (End)
%H Ray Chandler, <a href="/A124995/b124995.txt">Table of n, a(n) for n = 0..1114</a> (terms < 10^1000)
%H Ovidiu Bagdasar and Dorin Andrica, <a href="https://dx.doi.org/10.1109/ICMSAO.2017.7934928">New results and conjectures on 2-partitions of multisets</a>, 2017 7th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO).
%p seq(coeff(mul(x^k+1/x^k,k=1..n)^3,x,0),n=0..50); # _Robert Israel_, Nov 09 2017
%o (PARI) a(n) = polcoef(prod(k=1, n, (x^k + 1/x^k)^3), 0); \\ _Michel Marcus_, Jan 07 2021
%Y For constant term in expansion of Product_{ k = 1..n } (x^k + 1/x^k)^q for other values of q see A063865, A047653, A124996.
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Jul 12 2008