OFFSET
0,2
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..50
FORMULA
a(n) = 3/4 * binomial(2*n, n)^3 / (n+1) for n >= 1, with a(0) = 1.
a(n) = 3/4 * (2*n)!^3 / (n!^6 * (n+1)) for n >= 1.
PROG
(PARI) {a(n) = my(A=1, B=1, C=1); for(i=0, 2*n,
A = 1 + x*B*C +x*O(x^n);
B = 1 + y*A*C +y*O(y^n);
C = 1 + z*A*B +z*O(z^n));
polcoeff(polcoeff(polcoeff(A, n, x), n, y), n, z)}
for(n=0, 30, print1(a(n), ", "))
(PARI) /* Using binomial formula */
{a(n) = 0^n/4 + 3/4 * binomial(2*n, n)^3 / (n+1)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 12 2019
STATUS
approved