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

0,2

Comments

See A088956 for the definition of the hyperbinomial transform.

Links

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

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

Maple

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

Crossrefs

Column k=4 of A144303.

Sequence in context: A129890 A316158 A120733 * A144792 A291846 A255927

Adjacent sequences: A218493 A218494 A218495 * A218497 A218498 A218499

Keyword

nonn

Author

Alois P. Heinz, Oct 30 2012

Status

approved