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8th iteration of the hyperbinomial transform on the sequence of 1's.
3

%I #10 Jan 04 2019 13:49:10

%S 1,9,97,1233,18209,308129,5901489,126560849,3010775745,78805945665,

%T 2253470828561,69959985025841,2345132738183841,84468280694319713,

%U 3254988169237833585,133676275015986223569,5830402582814375609729,269227430712934320151169

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

%C See A088956 for the definition of the hyperbinomial transform.

%H Alois P. Heinz, <a href="/A218500/b218500.txt">Table of n, a(n) for n = 0..150</a>

%F E.g.f.: exp(x) * (-LambertW(-x)/x)^8.

%F a(n) = Sum_{j=0..n} 8 * (n-j+8)^(n-j-1) * C(n,j).

%F Hyperbinomial transform of A218499.

%F a(n) ~ 8*exp(8+exp(-1))*n^(n-1). - _Vaclav Kotesovec_, Oct 18 2013

%p a:= n-> add(8*(n-j+8)^(n-j-1)*binomial(n,j), j=0..n):

%p seq (a(n), n=0..20);

%t Table[Sum[8*(n-j+8)^(n-j-1)*Binomial[n,j],{j,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 18 2013 *)

%t 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 Column k=8 of A144303.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Oct 30 2012