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4th iteration of the hyperbinomial transform on the sequence of 1's.
3

%I #10 Aug 16 2013 11:54:09

%S 1,5,33,281,2993,38705,592489,10516441,212841889,4845154913,

%T 122664558905,3421333467689,104297273041969,3451364116327249,

%U 123251578626936841,4725537745859375705,193647372258547916609,8447809104669814884545,390938955429073736493145

%N 4th 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="/A218496/b218496.txt">Table of n, a(n) for n = 0..150</a>

%F E.g.f.: exp(x) * (-LambertW(-x)/x)^4.

%F a(n) = Sum_{j=0..n} 4 * (n-j+4)^(n-j-1) * C(n,j).

%F Hyperbinomial transform of A089464.

%F a(n) ~ 4*exp(4+exp(-1))*n^(n-1). - _Vaclav Kotesovec_, Aug 16 2013

%p a:= n-> add(4*(n-j+4)^(n-j-1)*binomial(n,j), j=0..n):

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

%Y Column k=4 of A144303.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Oct 30 2012