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%I #16 Mar 20 2023 04:31:32
%S 1,1,1,1,25,121,361,841,4201,25705,118441,423721,1628881,8065201,
%T 41225185,184416961,768211081,3420474121,16620237001,79922011465,
%U 364149052705,1638806098945,7655390077105,36739991161105,174363209490625,811840219629121,3790118889635521
%N Constant term in the expansion of (1 + x + y + z + 1/(x*y*z))^n.
%H Winston de Greef, <a href="/A361637/b361637.txt">Table of n, a(n) for n = 0..1429</a>
%F a(n) = n! * Sum_{k=0..floor(n/4)} 1/(k!^4 * (n-4*k)!).
%F G.f.: Sum_{k>=0} (4*k)!/k!^4 * x^(4*k)/(1-x)^(4*k+1).
%F From _Vaclav Kotesovec_, Mar 20 2023: (Start)
%F Recurrence: n^3*a(n) = (2*n - 1)*(2*n^2 - 2*n + 1)*a(n-1) - (n-1)*(6*n^2 - 12*n + 7)*a(n-2) + 2*(n-2)*(n-1)*(2*n - 3)*a(n-3) + 255*(n-3)*(n-2)*(n-1)*a(n-4).
%F a(n) ~ 5^(n + 3/2) / (2^(5/2) * Pi^(3/2) * n^(3/2)). (End)
%o (PARI) a(n) = n!*sum(k=0, n\4, 1/(k!^4*(n-4*k)!));
%Y Cf. A002426, A344560.
%Y Cf. A008977, A328725.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Mar 19 2023
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