A218500 8th iteration of the hyperbinomial transform on the sequence of 1's.

1, 9, 97, 1233, 18209, 308129, 5901489, 126560849, 3010775745, 78805945665, 2253470828561, 69959985025841, 2345132738183841, 84468280694319713, 3254988169237833585, 133676275015986223569, 5830402582814375609729, 269227430712934320151169

Offset: 0

Author

Alois P. Heinz, Oct 30 2012

Keywords

• nonn

Comments

See A088956 for the definition of the hyperbinomial transform.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150

Crossrefs

Column k=8 of A144303.

Programs

Maple

a:= n-> add(8*(n-j+8)^(n-j-1)*binomial(n,j), j=0..n):
seq (a(n), n=0..20);

Mathematica

Table[Sum[8*(n-j+8)^(n-j-1)*Binomial[n,j],{j,0,n}],{n,0,20}] (* Vaclav Kotesovec, Oct 18 2013 *)
With[{nn=20},CoefficientList[Series[Exp[x](-LambertW[-x]/x)^8,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jan 04 2019 *)

Formula

E.g.f.: exp(x) * (-LambertW(-x)/x)^8.

a(n) = Sum_{j=0..n} 8 * (n-j+8)^(n-j-1) * C(n,j).

Hyperbinomial transform of A218499.

a(n) ~ 8*exp(8+exp(-1))*n^(n-1). - Vaclav Kotesovec, Oct 18 2013