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A350282 a(n) is the constant term in the expansion of Product_{k=1..n} (x^k + 1/x^k)^n.

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%I A350282 #16 Dec 24 2021 02:34:10
%S A350282 1,0,4,62,4658,0,2319512420,14225426190522,361926393013029354,0,
%T A350282 16231015449888734994721650504,28330316118212024049511095643949434,
%U A350282 200866780133770636272812495083578779133456,0
%N A350282 a(n) is the constant term in the expansion of Product_{k=1..n} (x^k + 1/x^k)^n.
%C A350282 a(n) is the coefficient of x^(n^2 * (n+1)/2) in Product_{k=0..n} (1 + x^(2*k))^n.
%H A350282 Seiichi Manyama, <a href="/A350282/b350282.txt">Table of n, a(n) for n = 0..50</a>
%F A350282 a(4*n+1) = 0.
%o A350282 (PARI) a(n) = polcoef(prod(k=1, n, x^k+1/x^k)^n, 0);
%o A350282 (PARI) a(n) = polcoef(prod(k=1, n, 1+x^(2*k))^n, n^2*(n+1)/2);
%Y A350282 Cf. A063865, A047653, A124995, A124996.
%Y A350282 Cf. A350283.
%K A350282 nonn
%O A350282 0,3
%A A350282 _Seiichi Manyama_, Dec 23 2021