OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k=0..floor(n/2)} A104978(n-k, n-2*k).
a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-4*k, 3*n-5*k)*binomial(3*n-5*k, n-2*k)/(2*n-3*k+1).
G.f. satisfies: A(x) = 1 + x*A(x)^3 + x^2*A(x)^2. - Paul D. Hanna, May 27 2010
MATHEMATICA
Table[Sum[Binomial[3*n-4*k, 3*n-5*k]*Binomial[3*n-5*k, n-2*k]/(2*n-3*k+1), {k, 0, n/2}], {n, 0, 30}] (* G. C. Greubel, Jun 08 2021 *)
PROG
(PARI) {a(n)=sum(k=0, n\2, binomial(3*n-4*k, 3*n-5*k)*binomial(3*n-5*k, n-2*k)/(2*n-3*k+1))}
(Magma)
A104979:= func< n | (&+[Binomial(3*n-4*k, 3*n-5*k)*Binomial(3*n-5*k, n-2*k)/(2*n-3*k+1): k in [0..Floor(n/2)]]) >;
[A104979(n): n in [0..30]]; // G. C. Greubel, Jun 08 2021
(Sage)
def A104979(n): return sum( binomial(3*n-4*k, 3*n-5*k)*binomial(3*n-5*k, n-2*k)/(2*n-3*k+1) for k in (0..n//2) )
[A104979(n) for n in (0..30)] # G. C. Greubel, Jun 08 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 30 2005
STATUS
approved