A365032 - OEIS

%I #19 Dec 01 2024 10:51:47

%S 1,1,9,106,1949,47376,1443757,53003392,2278044729,112267072000,

%T 6242682602321,386708915902464,26411820455554261,1971959747016534016,

%U 159794005364013403125,13967707431203856449536,1310083060716906045342833,131245686122586065682628608

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

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

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

%F E.g.f.: (1/x) * Series_Reversion( x*exp(-x*(1 + x)^3) ). - _Seiichi Manyama_, Sep 23 2024

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

%Y Cf. A088695, A365031.

%Y Cf. A364940.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 17 2023