A377554 - OEIS

%I #9 Nov 01 2024 09:30:28

%S 1,3,30,537,14124,493695,21601458,1137294039,70064934600,

%T 4947238170747,394022075650590,34951812094581723,3417754921150904172,

%U 365287875167708973831,42368411854713294141834,5300422308901745571018735,711465905597330333014408848,101995745742232833085109746803

%N Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x*exp(x))^3 ).

%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)))^3.

%F E.g.f.: B(x)^3, where B(x) is the e.g.f. of A364986.

%F a(n) = (n!/(n+1)) * Sum_{k=0..n} k^(n-k) * binomial(3*n+3,k)/(n-k)!.

%o (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(3*n+3, k)/(n-k)!)/(n+1);

%Y Cf. A161633, A377553.

%Y Cf. A364986.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 01 2024