A380919 - OEIS

%I #9 Feb 08 2025 10:29:47

%S 1,4,55,1380,51213,2533968,157230099,11752365600,1028673637785,

%T 103250018926080,11693974366638639,1475530063767972864,

%U 205281631888995454245,31221155498006896773120,5153702313885813394180875,917695970480270443222536192,175344823710094148613399084849

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

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

%F E.g.f. A(x) satisfies A(x) = exp(3*x*A(x) / (1 - x*A(x))) / (1 - x*A(x)).

%F a(n) = n! * Sum_{k=0..n} 3^k * (n+1)^(k-1) * binomial(2*n,n-k)/k!.

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

%Y Cf. A380663, A380918.

%Y Cf. A380917.

%K nonn,new

%O 0,2

%A _Seiichi Manyama_, Feb 08 2025