cp's OEIS Frontend

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.

A326920 Constant term in the expansion of (-1 + Product_{k=1..n} (1 + x_k + 1/x_k))^n.

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%I A326920 #35 Oct 30 2019 08:17:02
%S A326920 1,0,8,264,121200,332810400,7753173594200,1440193875113407680,
%T A326920 2250630808138439243100640,29565964235758317208187044137600,
%U A326920 3307988125501026209547184198622507128848,3165738749695300492286911657015518806826344524560
%N A326920 Constant term in the expansion of (-1 + Product_{k=1..n} (1 + x_k + 1/x_k))^n.
%C A326920 Also number of n-step closed walks (from origin to origin) in n-dimensional lattice, using steps (t_1,t_2, ... ,t_n) (t_k = -1, 1 or 0 for 1 <= k <= n) except for (0,0, ... ,0) (t_k = 0 for 1 <= k <= n).
%H A326920 Seiichi Manyama, <a href="/A326920/b326920.txt">Table of n, a(n) for n = 0..47</a>
%F A326920 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A002426(k)^n.
%F A326920 a(n) ~ 3^(n^2 + n/2) / (exp(3/16) * 2^n * Pi^(n/2) * n^(n/2)). - _Vaclav Kotesovec_, Oct 30 2019
%t A326920 Table[Sum[(-1)^(n-k) * Binomial[n, k] * Sum[Binomial[k, 2*j]*Binomial[2*j, j], {j, 0, k}]^n, {k, 0, n}], {n, 0, 12}] (* _Vaclav Kotesovec_, Oct 30 2019 *)
%o A326920 (PARI) {a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*polcoef((1+x+1/x)^k, 0)^n)}
%Y A326920 Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A002426(k)^m: A126869 (m=1), A094061 (m=2), A328874 (m=3), A328875 (m=4).
%K A326920 nonn
%O A326920 0,3
%A A326920 _Seiichi Manyama_, Oct 29 2019