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

0,2

Comments

See A088956 for the definition of the hyperbinomial transform.

Links

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

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

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 *)

Crossrefs

Column k=8 of A144303.

Sequence in context: A180675 A083077 A194725 * A293986 A123821 A145509

Adjacent sequences: A218497 A218498 A218499 * A218501 A218502 A218503

Keyword

nonn

Author

Alois P. Heinz, Oct 30 2012

Status

approved