OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..79
FORMULA
Equals the antidiagonal sums of triangle A209330(n,k) = C(n^2,n*k).
Limit n->infinity a(n)^(1/n^2) = ((1-r)/r)^((1-r)^2/(3-4*r)) = 1.4360944969025357119535113523184471047971386419..., where r = A323777 = 0.220676041323740696312822269998050167187681031... is the root of the equation (1-2*r)^(3-4*r) = (1-r)^(2-2*r) * r^(1-2*r). - Vaclav Kotesovec, Mar 03 2014
MATHEMATICA
Table[Sum[Binomial[(n-k)^2, n*k-k^2], {k, 0, Floor[n/2]}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 03 2014 *)
PROG
(PARI) {a(n)=sum(k=0, n\2, binomial((n-k)^2, n*k-k^2))}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 06 2012
EXTENSIONS
Name corrected by Vaclav Kotesovec, Mar 03 2014
STATUS
approved