A218502 10th iteration of the hyperbinomial transform on the sequence of 1's.

1, 11, 141, 2081, 34961, 661601, 13970521, 326429401, 8377176001, 234573153281, 7125155956601, 233554674134441, 8223284332647361, 309711995280132001, 12430859603012736601, 529915231307371964201, 23918971999180778999681, 1139982481554110359552001

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)^10.

a(n) = Sum_{j=0..n} 10 * (n-j+10)^(n-j-1) * C(n,j).

Hyperbinomial transform of A218501.

a(n) ~ 10*exp(10+exp(-1))*n^(n-1). - Vaclav Kotesovec, Oct 18 2013

Maple

a:= n-> add(10*(n-j+10)^(n-j-1)*binomial(n, j), j=0..n):
seq (a(n), n=0..20);

Mathematica

Table[Sum[10*(n-j+10)^(n-j-1)*Binomial[n, j], {j, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 18 2013 *)

Crossrefs

Column k=10 of A144303.

Sequence in context: A205084 A083078 A048965 * A293988 A024141 A289216

Adjacent sequences: A218499 A218500 A218501 * A218503 A218504 A218505

Keyword

nonn

Author

Alois P. Heinz, Oct 30 2012

Status

approved