OFFSET
0,3
FORMULA
G.f. satisfies A(x) = 1 + x*A(x)^6 / (1 + x*A(x)^4).
a(n) = (1/n) * Sum_{k=0..n-1} binomial(n,k) * binomial(4*n+k,n-1-k) for n > 0.
a(n) = (1/n) * Sum_{k=0..n-1} (-1)^k * binomial(n,k) * binomial(6*n-2*k,n-1-k) for n > 0.
a(n) = (1/n) * Sum_{k=0..floor(n-1)/2} binomial(n,k) * binomial(5*n-k,n-1-2*k) for n > 0. - Seiichi Manyama, Apr 01 2024
PROG
(PARI) a(n) = if(n==0, 1, sum(k=0, n-1, binomial(n, k)*binomial(4*n+k, n-1-k))/n);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 06 2023
STATUS
approved