login
5th iteration of the hyperbinomial transform on the sequence of 1's.
3

%I #8 Oct 18 2013 15:12:26

%S 1,6,46,441,5156,71801,1166886,21756251,458803176,10814534541,

%T 282098765426,8074875680471,251807768368956,8501320507058801,

%U 309046115586282726,12039399243732745851,500492026353038459216,22119195334250297991701,1035767312348853244634586

%N 5th 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="/A218497/b218497.txt">Table of n, a(n) for n = 0..150</a>

%F E.g.f.: exp(x) * (-LambertW(-x)/x)^5.

%F a(n) = Sum_{j=0..n} 5 * (n-j+5)^(n-j-1) * C(n,j).

%F Hyperbinomial transform of A218496.

%F a(n) ~ 5*exp(5+exp(-1))*n^(n-1). - _Vaclav Kotesovec_, Oct 18 2013

%p a:= n-> add(5*(n-j+5)^(n-j-1)*binomial(n,j), j=0..n):

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

%t Table[Sum[5*(n-j+5)^(n-j-1)*Binomial[n,j],{j,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 18 2013 *)

%Y Column k=5 of A144303.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Oct 30 2012