OFFSET
0,3
COMMENTS
Equals the antidiagonal sums of triangle A228836.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..86
FORMULA
Limit n->infinity a(n)^(1/n^2) = ((1-r)^2/(r*(1-2*r)))^((1-3*r)*(1-r)/(3*(1-2*r))) = 1.36198508972775011599..., where r = 0.195220321930105755... is the root of the equation (1-3*r+3*r^2)^(3*(2*r-1)) = (r*(1-2*r))^(4*r-1) * (1-r)^(4*(r-1)). - Vaclav Kotesovec, added Sep 05 2013, simplified Mar 04 2014
MATHEMATICA
Table[Sum[Binomial[(n-k)^2, (n-2*k)*k], {k, 0, Floor[n/2]}], {n, 0, 15}] (* Vaclav Kotesovec, Sep 05 2013 *)
PROG
(PARI) {a(n)=sum(k=0, n\2, binomial((n-k)^2, (n-2*k)*k))}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 05 2013
STATUS
approved