A377576 - OEIS

%I #10 Nov 02 2024 09:11:46

%S 1,4,52,1116,34408,1394340,70298424,4248802516,299752943200,

%T 24196951718532,2200519882434280,222683725755611604,

%U 24824104612186789584,3023063956714780554628,399343825987950226379416,56879649386095684434783060,8689968793295620150120679104

%N E.g.f. satisfies A(x) = (1 + x * exp(x) * A(x))^4.

%F E.g.f.: B(x)^4, where B(x) is the e.g.f. of A364987.

%F a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(4*k+4,k)/( (k+1)*(n-k)! ).

%o (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(4*k+4, k)/((k+1)*(n-k)!));

%Y Cf. A006153, A377574, A377575.

%Y Cf. A364987, A377577.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 02 2024