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A218499 7th iteration of the hyperbinomial transform on the sequence of 1's. 3
1, 8, 78, 911, 12524, 199403, 3624706, 74300269, 1699264792, 42964199279, 1191492782054, 35994106307321, 1177389200637028, 41482632276082915, 1566911405137366450, 63190697224460246477, 2710704012199936430000, 123277690401078017104343, 5925900498827152433216446 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 18 15:33 EST 2018. Contains 299324 sequences. (Running on oeis4.)