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6th iteration of the hyperbinomial transform on the sequence of 1's.
3

%I #8 Oct 18 2013 15:12:44

%S 1,7,61,649,8257,123217,2120545,41484625,911339617,22249542241,

%T 598364232529,17591851634353,561695417002225,19366094448215665,

%U 717377453802538753,28423991158962139873,1199873992182732076225,53772852099331738315969,2550272224743737587911025

%N 6th 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="/A218498/b218498.txt">Table of n, a(n) for n = 0..150</a>

%F E.g.f.: exp(x) * (-LambertW(-x)/x)^6.

%F a(n) = A(n,k) = Sum_{j=0..n} 6 * (n-j+6)^(n-j-1) * C(n,j).

%F Hyperbinomial transform of A218497.

%F a(n) ~ 6*exp(6+exp(-1))*n^(n-1). - _Vaclav Kotesovec_, Oct 18 2013

%p a:= n-> add(6*(n-j+6)^(n-j-1)*binomial(n,j), j=0..n):

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

%t Table[Sum[6*(n-j+6)^(n-j-1)*Binomial[n,j],{j,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 18 2013 *)

%Y Column k=6 of A144303.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Oct 30 2012