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

0,2

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)^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

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 *)

Crossrefs

Column k=6 of A144303.

Sequence in context: A111532 A061634 A049402 * A261687 A001830 A213326

Adjacent sequences: A218495 A218496 A218497 * A218499 A218500 A218501

Keyword

nonn

Author

Alois P. Heinz, Oct 30 2012

Status

approved