A209428 a(n) = Sum_{k=0..[n/2]} binomial(n-k,k)^(n-k).

1, 1, 2, 5, 29, 284, 4423, 146913, 12314170, 1881868883, 442540106327, 198351607585964, 242843144659704443, 641109494638274737567, 2641514784666925880476348, 17914201815999230497003603969, 302266027138470510426936352722523

Offset

0,3

Comments

Equals antidiagonal sums of triangle A209427.

Links

G. C. Greubel, Table of n, a(n) for n = 0..82

Formula

Limit n->infinity a(n)^(1/n^2) = ((1-r)/r)^((1-r)^2/(3-4*r)) = 1.4360944969025357119535113523184471..., where r = A323777 = 0.220676041323740696312822269998... is the root of the equation (1-2*r)^(3-4*r) = (1-r)^(2-2*r) * r^(1-2*r). - Vaclav Kotesovec, Mar 06 2014

Mathematica

Table[Sum[Binomial[n-k, k]^(n-k), {k, 0, Floor[n/2]}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 06 2014 *)

Prog

(PARI) {a(n)=sum(k=0, n\2, binomial(n-k, k)^(n-k))}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A209427, A209331.

Sequence in context: A108367 A191621 A103592 * A098026 A179823 A064098

Adjacent sequences: A209425 A209426 A209427 * A209429 A209430 A209431

Keyword

nonn

Author

Paul D. Hanna, Mar 08 2012

Status

approved