A376563 - OEIS

%I #11 Sep 28 2024 10:42:32

%S 1,1,3,16,149,2016,34447,697264,16349769,438688000,13302715931,

%T 450127632384,16805250091357,685963808029696,30389466219654375,

%U 1452343581621354496,74484586717220845073,4080558161067766972416,237830597688699873580339,14694357436059217272832000

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

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

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

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

%o (PARI) a(n) = n!*sum(k=0, n\3, (n+1)^(n-3*k-1)*binomial(n-2*k-1, k)/(n-3*k)!);

%Y Cf. A052873, A376558.

%Y Cf. A293493, A376475.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 28 2024