login
A365267
G.f. satisfies A(x) = 1 + x*A(x)^2*(1 + x^3*A(x)).
1
1, 1, 2, 5, 15, 47, 153, 513, 1763, 6177, 21981, 79224, 288611, 1061019, 3931320, 14666135, 55041855, 207668702, 787225265, 2996851140, 11452198368, 43915195973, 168930713580, 651708006690, 2520840672423, 9774511167507, 37985839339052
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k,k) * binomial(2*n-5*k+1,n-3*k)/(2*n-5*k+1).
PROG
(PARI) a(n) = sum(k=0, n\4, binomial(n-3*k, k)*binomial(2*n-5*k+1, n-3*k)/(2*n-5*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 30 2023
STATUS
approved