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A218500 8th iteration of the hyperbinomial transform on the sequence of 1's.

%I A218500 #10 Jan 04 2019 13:49:10
%S A218500 1,9,97,1233,18209,308129,5901489,126560849,3010775745,78805945665,
%T A218500 2253470828561,69959985025841,2345132738183841,84468280694319713,
%U A218500 3254988169237833585,133676275015986223569,5830402582814375609729,269227430712934320151169
%N A218500 8th iteration of the hyperbinomial transform on the sequence of 1's.
%C A218500 See A088956 for the definition of the hyperbinomial transform.
%H A218500 Alois P. Heinz, <a href="/A218500/b218500.txt">Table of n, a(n) for n = 0..150</a>
%F A218500 E.g.f.: exp(x) * (-LambertW(-x)/x)^8.
%F A218500 a(n) = Sum_{j=0..n} 8 * (n-j+8)^(n-j-1) * C(n,j).
%F A218500 Hyperbinomial transform of A218499.
%F A218500 a(n) ~ 8*exp(8+exp(-1))*n^(n-1). - _Vaclav Kotesovec_, Oct 18 2013
%p A218500 a:= n-> add(8*(n-j+8)^(n-j-1)*binomial(n,j), j=0..n):
%p A218500 seq (a(n), n=0..20);
%t A218500 Table[Sum[8*(n-j+8)^(n-j-1)*Binomial[n,j],{j,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 18 2013 *)
%t A218500 With[{nn=20},CoefficientList[Series[Exp[x](-LambertW[-x]/x)^8,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jan 04 2019 *)
%Y A218500 Column k=8 of A144303.
%K A218500 nonn
%O A218500 0,2
%A A218500 _Alois P. Heinz_, Oct 30 2012