%I #24 May 06 2021 03:11:34
%S 1,2,10,164,9826,2031252,1622278624,4579408029576,51207103076632066,
%T 2052124795850957537060,330463219813679264204224300,
%U 192454957455454582636391397662856,454577215426865313388106323928590128736,3907905904547764847197154889183844343802986600
%N Constant term in the expansion of (Product_{k=1..n} (1 + x_k) + Product_{k=1..n} (1 + 1/x_k))^n.
%H Seiichi Manyama, <a href="/A328812/b328812.txt">Table of n, a(n) for n = 0..58</a>
%F a(n) = A309010(n,n+1) = Sum_{k=0..n} binomial(n,k)^(n+1).
%F a(n) ~ c * exp(-1/4) * 2^((2*n+1)*(n+1)/2) / (Pi*n)^((n+1)/2), where c = A218792 = Sum_{k = -infinity..infinity} exp(-2*k^2) = 1.271341522189... and c = Sum_{k = -infinity..infinity} exp(-2*(k+1/2)^2) = 1.23528676585389... if n is odd. - _Vaclav Kotesovec_, May 06 2021
%t a[n_] := Sum[Binomial[n, k]^(n + 1), {k, 0, n}]; Array[a, 14, 0] (* _Amiram Eldar_, May 06 2021 *)
%o (PARI) {a(n) = sum(k=0, n, binomial(n, k)^(n+1))}
%Y Cf. A167010, A309010, A328813, A328814.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Oct 28 2019