A218497 5th iteration of the hyperbinomial transform on the sequence of 1's.

1, 6, 46, 441, 5156, 71801, 1166886, 21756251, 458803176, 10814534541, 282098765426, 8074875680471, 251807768368956, 8501320507058801, 309046115586282726, 12039399243732745851, 500492026353038459216, 22119195334250297991701, 1035767312348853244634586

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)^5.

a(n) = Sum_{j=0..n} 5 * (n-j+5)^(n-j-1) * C(n,j).

Hyperbinomial transform of A218496.

a(n) ~ 5*exp(5+exp(-1))*n^(n-1). - Vaclav Kotesovec, Oct 18 2013

Maple

a:= n-> add(5*(n-j+5)^(n-j-1)*binomial(n, j), j=0..n):
seq (a(n), n=0..20);

Mathematica

Table[Sum[5*(n-j+5)^(n-j-1)*Binomial[n, j], {j, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 18 2013 *)

Crossrefs

Column k=5 of A144303.

Sequence in context: A284109 A049378 A365056 * A261499 A001829 A006386

Adjacent sequences: A218494 A218495 A218496 * A218498 A218499 A218500

Keyword

nonn

Author

Alois P. Heinz, Oct 30 2012

Status

approved