A218496 4th iteration of the hyperbinomial transform on the sequence of 1's.

1, 5, 33, 281, 2993, 38705, 592489, 10516441, 212841889, 4845154913, 122664558905, 3421333467689, 104297273041969, 3451364116327249, 123251578626936841, 4725537745859375705, 193647372258547916609, 8447809104669814884545, 390938955429073736493145

Offset: 0

Author

Alois P. Heinz, Oct 30 2012

Keywords

• nonn

Comments

See A088956 for the definition of the hyperbinomial transform.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150

Crossrefs

Column k=4 of A144303.

Programs

Maple

a:= n-> add(4*(n-j+4)^(n-j-1)*binomial(n,j), j=0..n):
seq (a(n), n=0..20);

Formula

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

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

Hyperbinomial transform of A089464.

a(n) ~ 4*exp(4+exp(-1))*n^(n-1). - Vaclav Kotesovec, Aug 16 2013