This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A328812 #24 May 06 2021 03:11:34 %S A328812 1,2,10,164,9826,2031252,1622278624,4579408029576,51207103076632066, %T A328812 2052124795850957537060,330463219813679264204224300, %U A328812 192454957455454582636391397662856,454577215426865313388106323928590128736,3907905904547764847197154889183844343802986600 %N A328812 Constant term in the expansion of (Product_{k=1..n} (1 + x_k) + Product_{k=1..n} (1 + 1/x_k))^n. %H A328812 Seiichi Manyama, <a href="/A328812/b328812.txt">Table of n, a(n) for n = 0..58</a> %F A328812 a(n) = A309010(n,n+1) = Sum_{k=0..n} binomial(n,k)^(n+1). %F A328812 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 A328812 a[n_] := Sum[Binomial[n, k]^(n + 1), {k, 0, n}]; Array[a, 14, 0] (* _Amiram Eldar_, May 06 2021 *) %o A328812 (PARI) {a(n) = sum(k=0, n, binomial(n, k)^(n+1))} %Y A328812 Cf. A167010, A309010, A328813, A328814. %K A328812 nonn %O A328812 0,2 %A A328812 _Seiichi Manyama_, Oct 28 2019