A379867 - OEIS

%I #18 Jan 05 2025 09:58:34

%S 1,2,23,529,18589,884281,53195407,3874595089,331580316473,

%T 32614443047521,3625839880813171,449629404853604185,

%U 61535275741655857621,9213155228282408405185,1498018121369750569371959,262869047482982449625840161,49515850496472530668242845041

%N E.g.f. A(x) satisfies A(x) = 1/(exp(-x*A(x)^2) - x*A(x)^2).

%F E.g.f.: sqrt( (1/x) * Series_Reversion( x * (exp(-x) - x)^2 ) ).

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

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

%Y Cf. A377890, A379870.

%Y Cf. A377892, A379884.

%Y Cf. A377891, A377893, A379886.

%Y Cf. A364985, A379864.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 04 2025