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A361703 Constant term in the expansion of (1 + w + x + y + z + 1/(w*x*y*z))^n.

%I A361703 #22 Jul 04 2025 10:04:39
%S A361703 1,1,1,1,1,121,721,2521,6721,15121,143641,1302841,7579441,32586841,
%T A361703 113753641,509068561,3599319361,25076993761,142188273361,662296228561,
%U A361703 2933770097881,15581813723281,99333170493481,623696622059281,3466773281312881,17406784944114721
%N A361703 Constant term in the expansion of (1 + w + x + y + z + 1/(w*x*y*z))^n.
%C A361703 Diagonal of the rational function 1/(1 - (v^5 + w^5 + x^5 + y^5 + z^5 + v*w*x*y*z)). - _Seiichi Manyama_, Jul 04 2025
%H A361703 Seiichi Manyama, <a href="/A361703/b361703.txt">Table of n, a(n) for n = 0..1000</a>
%F A361703 a(n) = Sum_{k=0..floor(n/5)} (4*k)!/k!^4 * binomial(5*k,4*k) * binomial(n,5*k) = Sum_{k=0..floor(n/5)} (5*k)!/k!^5 * binomial(n,5*k).
%F A361703 a(n) ~ 9 * 6^n / (sqrt(5) * Pi^2 * n^2). - _Vaclav Kotesovec_, Mar 25 2023
%o A361703 (PARI) a(n) = sum(k=0, n\5, (4*k)!/k!^4*binomial(5*k, 4*k)*binomial(n, 5*k));
%Y A361703 Cf. A361675, A361704, A361705.
%Y A361703 Cf. A002426, A344560, A361637.
%Y A361703 Cf. A082489, A361636.
%K A361703 nonn,easy
%O A361703 0,6
%A A361703 _Seiichi Manyama_, Mar 21 2023