A377630 - OEIS

%I #10 Nov 03 2024 09:32:15

%S 1,4,52,1212,41512,1889700,107684664,7384011796,592485333472,

%T 54488274328836,5652345176418280,653054114586249684,

%U 83175314479016845584,11578838832843098353732,1749242011108507789948312,285034599164755404426493140,49833544890911336997795542464

%N Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x*exp(x))^4 ).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

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

%F E.g.f.: B(x)^4, where B(x) is the e.g.f. of A364989.

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

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

%Y Cf. A161633, A377553, A377554.

%Y Cf. A364989, A377633.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 02 2024