A376124 - OEIS

%I #12 Sep 11 2024 10:04:45

%S 0,1,8,117,2584,77245,2923776,134147881,7237959296,449153207001,

%T 31518672486400,2468063119978621,213353171897306112,

%U 20181854221412587093,2073632053555295657984,229977288184566078752625,27382787929802599713243136,3483970698377702965413968689

%N E.g.f. A(x) satisfies A(x) = x * exp(A(x)) * (1 + 3*A(x)).

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

%F E.g.f.: Series_Reversion( x * exp(-x) / (1 + 3*x) ).

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

%F a(n) ~ ((7 + sqrt(13))/2)^n * n^(n-1) / (13^(1/4) * exp((7 - sqrt(13))*n/6)). - _Vaclav Kotesovec_, Sep 11 2024

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

%Y Cf. A052885, A376123.

%Y Cf. A376094, A376101.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 11 2024