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

%I A218501 #8 Oct 18 2013 15:11:37
%S A218501 1,10,118,1621,25588,458605,9232894,206835751,5113191304,138473150833,
%T A218501 4081818946330,130223467785619,4473867764956204,164772507070721989,
%U A218501 6479598382677480286,271083794667222927655,12026359894442420178064,564099525344446492486105
%N A218501 9th iteration of the hyperbinomial transform on the sequence of 1's.
%C A218501 See A088956 for the definition of the hyperbinomial transform.
%H A218501 Alois P. Heinz, <a href="/A218501/b218501.txt">Table of n, a(n) for n = 0..150</a>
%F A218501 E.g.f.: exp(x) * (-LambertW(-x)/x)^9.
%F A218501 a(n) = Sum_{j=0..n} 9 * (n-j+9)^(n-j-1) * C(n,j).
%F A218501 Hyperbinomial transform of A218500.
%F A218501 a(n) ~ 9*exp(9+exp(-1))*n^(n-1). - _Vaclav Kotesovec_, Oct 18 2013
%p A218501 a:= n-> add(9*(n-j+9)^(n-j-1)*binomial(n,j), j=0..n):
%p A218501 seq (a(n), n=0..20);
%t A218501 Table[Sum[9*(n-j+9)^(n-j-1)*Binomial[n,j],{j,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 18 2013 *)
%Y A218501 Column k=9 of A144303.
%K A218501 nonn
%O A218501 0,2
%A A218501 _Alois P. Heinz_, Oct 30 2012