A218499 7th iteration of the hyperbinomial transform on the sequence of 1's.

1, 8, 78, 911, 12524, 199403, 3624706, 74300269, 1699264792, 42964199279, 1191492782054, 35994106307321, 1177389200637028, 41482632276082915, 1566911405137366450, 63190697224460246477, 2710704012199936430000, 123277690401078017104343, 5925900498827152433216446

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=7 of A144303.

Programs

Maple

a:= n-> add(7*(n-j+7)^(n-j-1)*binomial(n,j), j=0..n):
seq (a(n), n=0..20);

Mathematica

Table[Sum[7*(n-j+7)^(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)^7.

a(n) = Sum_{j=0..n} 7 * (n-j+7)^(n-j-1) * C(n,j).

Hyperbinomial transform of A218498.

a(n) ~ 7*exp(7+exp(-1))*n^(n-1). - Vaclav Kotesovec, Oct 18 2013