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 A361705 #11 Mar 25 2023 07:12:09 %S A361705 1,1,1,1,1,1,1,1,1681,15121,75601,277201,831601,2162161,5045041, %T A361705 10810801,54054001,592191601,5035670641,31553973361,157346607601, %U A361705 660308770801,2420415874801,7951853614321,24853781309281,91246800876001,497098157556001,3346262924004001 %N A361705 Constant term in the expansion of (1 + w^4 + x^4 + y^4 + z^4 + 1/(w*x*y*z))^n. %F A361705 a(n) = Sum_{k=0..floor(n/8)} (4*k)!/k!^4 * binomial(8*k,4*k) * binomial(n,8*k). %F A361705 a(n) ~ 5^(n+2) / (2^(5/2) * Pi^2 * n^2). - _Vaclav Kotesovec_, Mar 25 2023 %t A361705 Table[Sum[(4*k)!/k!^4 * Binomial[8*k,4*k] * Binomial[n,8*k], {k,0,n/8}], {n,0,30}] (* _Vaclav Kotesovec_, Mar 25 2023 *) %o A361705 (PARI) a(n) = sum(k=0, n\8, (4*k)!/k!^4*binomial(8*k, 4*k)*binomial(n, 8*k)); %Y A361705 Cf. A361675, A361703, A361704. %Y A361705 Cf. A361657, A361658. %K A361705 nonn,easy %O A361705 0,9 %A A361705 _Seiichi Manyama_, Mar 21 2023