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

Author

Paul D. Hanna, Mar 08 2012

Keywords

• nonn

Comments

Equals antidiagonal sums of triangle A209427.

Links

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

Crossrefs

Cf. A209427, A209331.

Programs

Mathematica

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

PARI

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

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