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A218501 9th iteration of the hyperbinomial transform on the sequence of 1's. 3
1, 10, 118, 1621, 25588, 458605, 9232894, 206835751, 5113191304, 138473150833, 4081818946330, 130223467785619, 4473867764956204, 164772507070721989, 6479598382677480286, 271083794667222927655, 12026359894442420178064, 564099525344446492486105 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
See A088956 for the definition of the hyperbinomial transform.
LINKS
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: A309582 A155622 A307695 * A293987 A122887 A284331
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 30 2012
STATUS
approved

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)