OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Vaclav Kotesovec, Recurrence
FORMULA
a(n) = Sum_{k=0..n} C(2*n-k+1,k)/(n-k+1) * C(n+2*k-1,n-k).
Let A(x)^m = Sum_{n>=0} a(n,m)*x^n then
a(n,m) = Sum_{k=0..n} C(2*n-k+m,k)*m/(n-k+m) * C(n+2*k-1,n-k).
a(n) ~ c*d^n/(sqrt(Pi)*n^(3/2)), where d = 8.01957328653868383... is the root of the equation 3125 + 22356*d - 162432*d^2 - 361584*d^3 - 326592*d^4 + 46656*d^5 = 0 and c = 1.216730444416766043545857948227854793382399566... - Vaclav Kotesovec, Sep 18 2013
MATHEMATICA
Table[Sum[Binomial[2*n-k+1, k]/(n-k+1)*Binomial[n+2*k-1, n-k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 18 2013 *)
PROG
(PARI) {a(n, m=1)=sum(k=0, n, binomial(2*n-k+m, k)*m/(n-k+m)*binomial(n+2*k-1, n-k))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 19 2009
STATUS
approved