A218498 6th iteration of the hyperbinomial transform on the sequence of 1's.

1, 7, 61, 649, 8257, 123217, 2120545, 41484625, 911339617, 22249542241, 598364232529, 17591851634353, 561695417002225, 19366094448215665, 717377453802538753, 28423991158962139873, 1199873992182732076225, 53772852099331738315969, 2550272224743737587911025

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=6 of A144303.

Programs

Maple

a:= n-> add(6*(n-j+6)^(n-j-1)*binomial(n,j), j=0..n):
seq (a(n), n=0..20);

Mathematica

Table[Sum[6*(n-j+6)^(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)^6.

a(n) = A(n,k) = Sum_{j=0..n} 6 * (n-j+6)^(n-j-1) * C(n,j).

Hyperbinomial transform of A218497.

a(n) ~ 6*exp(6+exp(-1))*n^(n-1). - Vaclav Kotesovec, Oct 18 2013