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

0,2

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)^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

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 *)

Crossrefs

Column k=7 of A144303.

Sequence in context: A091106 A199758 A111533 * A132164 A058480 A000435

Adjacent sequences: A218496 A218497 A218498 * A218500 A218501 A218502

Keyword

nonn

Author

Alois P. Heinz, Oct 30 2012

Status

approved