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A218499 7th iteration of the hyperbinomial transform on the sequence of 1's.

%I A218499 #8 Oct 18 2013 15:14:09
%S A218499 1,8,78,911,12524,199403,3624706,74300269,1699264792,42964199279,
%T A218499 1191492782054,35994106307321,1177389200637028,41482632276082915,
%U A218499 1566911405137366450,63190697224460246477,2710704012199936430000,123277690401078017104343,5925900498827152433216446
%N A218499 7th iteration of the hyperbinomial transform on the sequence of 1's.
%C A218499 See A088956 for the definition of the hyperbinomial transform.
%H A218499 Alois P. Heinz, <a href="/A218499/b218499.txt">Table of n, a(n) for n = 0..150</a>
%F A218499 E.g.f.: exp(x) * (-LambertW(-x)/x)^7.
%F A218499 a(n) = Sum_{j=0..n} 7 * (n-j+7)^(n-j-1) * C(n,j).
%F A218499 Hyperbinomial transform of A218498.
%F A218499 a(n) ~ 7*exp(7+exp(-1))*n^(n-1). - _Vaclav Kotesovec_, Oct 18 2013
%p A218499 a:= n-> add(7*(n-j+7)^(n-j-1)*binomial(n,j), j=0..n):
%p A218499 seq (a(n), n=0..20);
%t A218499 Table[Sum[7*(n-j+7)^(n-j-1)*Binomial[n,j],{j,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 18 2013 *)
%Y A218499 Column k=7 of A144303.
%K A218499 nonn
%O A218499 0,2
%A A218499 _Alois P. Heinz_, Oct 30 2012