A218501 9th iteration of the hyperbinomial transform on the sequence of 1's.

1, 10, 118, 1621, 25588, 458605, 9232894, 206835751, 5113191304, 138473150833, 4081818946330, 130223467785619, 4473867764956204, 164772507070721989, 6479598382677480286, 271083794667222927655, 12026359894442420178064, 564099525344446492486105

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=9 of A144303.

Programs

Maple

a:= n-> add(9*(n-j+9)^(n-j-1)*binomial(n,j), j=0..n):
seq (a(n), n=0..20);

Mathematica

Table[Sum[9*(n-j+9)^(n-j-1)*Binomial[n,j],{j,0,n}],{n,0,20}] (* Vaclav Kotesovec, Oct 18 2013 *)

Formula

E.g.f.: exp(x) * (-LambertW(-x)/x)^9.

a(n) = Sum_{j=0..n} 9 * (n-j+9)^(n-j-1) * C(n,j).

Hyperbinomial transform of A218500.

a(n) ~ 9*exp(9+exp(-1))*n^(n-1). - Vaclav Kotesovec, Oct 18 2013