A379867 E.g.f. A(x) satisfies A(x) = 1/(exp(-x*A(x)^2) - x*A(x)^2).

1, 2, 23, 529, 18589, 884281, 53195407, 3874595089, 331580316473, 32614443047521, 3625839880813171, 449629404853604185, 61535275741655857621, 9213155228282408405185, 1498018121369750569371959, 262869047482982449625840161, 49515850496472530668242845041

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

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

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

Prog

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

Crossrefs

Cf. A377890, A379870.

Cf. A377892, A379884.

Cf. A377891, A377893, A379886.

Cf. A364985, A379864.

Sequence in context: A053161 A380726 A090731 * A090314 A379912 A084322

Adjacent sequences: A379864 A379865 A379866 * A379868 A379869 A379870

Keyword

nonn

Author

Seiichi Manyama, Jan 04 2025

Status

approved