login
A377630
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x*exp(x))^4 ).
1
1, 4, 52, 1212, 41512, 1889700, 107684664, 7384011796, 592485333472, 54488274328836, 5652345176418280, 653054114586249684, 83175314479016845584, 11578838832843098353732, 1749242011108507789948312, 285034599164755404426493140, 49833544890911336997795542464
OFFSET
0,2
FORMULA
E.g.f. satisfies A(x) = (1 + x * A(x) * exp(x*A(x)))^4.
E.g.f.: B(x)^4, where B(x) is the e.g.f. of A364989.
a(n) = (n!/(n+1)) * Sum_{k=0..n} k^(n-k) * binomial(4*n+4,k)/(n-k)!.
PROG
(PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(4*n+4, k)/(n-k)!)/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 02 2024
STATUS
approved