OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
SeoungJi Hong and SeungKyung Park, Hybrid d-ary trees and their generalization, Bull. Korean Math. Soc. 51 (2014), No. 1, pp. 229-235
FORMULA
a(n) = 1/(n^2+1) * Sum_{i=0..n} C(n^2+i,i) * C(n^2+i+1,n-i).
a(n) = [x^n] ((1+x)/(1-x-x^2))^(n^2+1) / (n^2+1).
a(n) = A245049(n,n+1).
a(n) ~ 2^(n-1/2) * exp(n+1/4) * n^(n-5/2) / sqrt(Pi). - Vaclav Kotesovec, Jul 11 2014
MAPLE
a:= n-> add(binomial(n^2+i, i)*binomial(n^2+i+1, n-i), i=0..n)/(n^2+1):
seq(a(n), n=0..20);
MATHEMATICA
Table[Sum[Binomial[n^2+i, i]*Binomial[n^2+i+1, n-i], {i, 0, n}]/(n^2+1), {n, 0, 20}] (* Vaclav Kotesovec, Jul 11 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 10 2014
STATUS
approved