A382037 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * B(x)^3) ), where B(x) = 1 + x*B(x)^3 is the g.f. of A001764.

1, 1, 9, 160, 4325, 157896, 7280077, 406085632, 26599741065, 2001864880000, 170236619802161, 16144762562002944, 1689534516295056301, 193403842876754728960, 24040636567791329323125, 3224829927677539092791296, 464325325579881390473331473, 71428455280041816247241637888

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

E.g.f. A(x) satisfies A(x) = exp(x*A(x) * B(x*A(x))^3).

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

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

Prog

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

Crossrefs

Cf. A052873, A382036, A382038.

Cf. A001764, A377830, A382033.

Sequence in context: A360777 A309472 A060348 * A365016 A367163 A363479

Adjacent sequences: A382034 A382035 A382036 * A382038 A382039 A382040

Keyword

nonn

Author

Seiichi Manyama, Mar 12 2025

Status

approved