A089468 Hyperbinomial transform of A089467 and also the 2nd hyperbinomial transform of A089466.

1, 3, 15, 110, 1083, 13482, 203569, 3618540, 74058105, 1715620148, 44384718879, 1268498827752, 39692276983555, 1349678904881400, 49556966130059553, 1954156038072106448, 82363978221026323761, 3695194039210436996400

Offset

0,2

Comments

See A088956 for the definition of the hyperbinomial transform.

Links

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

Formula

a(n) = sum(k=0, n, (n-k+1)^(n-k-1)*C(n, k)*A089467(k)). a(n) = sum(k=0, n, 2*(n-k+2)^(n-k-1)*C(n, k)*A089466(k)). a(n) = sum(m=0, n, sum(j=0, m, C(m, j)*C(n, n-m-j)*(n+1)^(n-m-j)*(m+j)!/(-2)^j)/m!)).

E.g.f.: (LambertW(-x)^2*exp(-1/2*LambertW(-x)^2))/(x^2*(1+LambertW(-x))). - Vladeta Jovovic, Oct 26 2004

a(n) ~ exp(3/2)*n^n. - Vaclav Kotesovec, Jul 09 2013

Mathematica

CoefficientList[Series[(LambertW[-x]^2*E^(-1/2*LambertW[-x]^2))/(x^2*(1+LambertW[-x])), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jul 09 2013 *)

Prog

(PARI) a(n)=if(n<0, 0, sum(m=0, n, sum(j=0, m, binomial(m, j)*binomial(n, n-m-j)*(n+1)^(n-m-j)*(m+j)!/(-2)^j)/m!))

Crossrefs

Cf. A089466, A089467, A088956.

Sequence in context: A054201 A090355 A083483 * A109498 A142967 A360864

Adjacent sequences: A089465 A089466 A089467 * A089469 A089470 A089471

Keyword

nonn

Author

Paul D. Hanna, Nov 08 2003

Status

approved