A218501 9th iteration of the hyperbinomial transform on the sequence of 1's.

1, 10, 118, 1621, 25588, 458605, 9232894, 206835751, 5113191304, 138473150833, 4081818946330, 130223467785619, 4473867764956204, 164772507070721989, 6479598382677480286, 271083794667222927655, 12026359894442420178064, 564099525344446492486105

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)^9.

a(n) = Sum_{j=0..n} 9 * (n-j+9)^(n-j-1) * C(n,j).

Hyperbinomial transform of A218500.

a(n) ~ 9*exp(9+exp(-1))*n^(n-1). - Vaclav Kotesovec, Oct 18 2013

Maple

a:= n-> add(9*(n-j+9)^(n-j-1)*binomial(n, j), j=0..n):
seq (a(n), n=0..20);

Mathematica

Table[Sum[9*(n-j+9)^(n-j-1)*Binomial[n, j], {j, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 18 2013 *)

Crossrefs

Column k=9 of A144303.

Sequence in context: A367779 A155622 A307695 * A293987 A122887 A284331

Adjacent sequences: A218498 A218499 A218500 * A218502 A218503 A218504

Keyword

nonn

Author

Alois P. Heinz, Oct 30 2012

Status

approved