login
A365186
G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x*A(x)^2).
7
1, 1, 6, 47, 428, 4241, 44407, 483358, 5414618, 62014112, 722870120, 8547768832, 102284029963, 1236274747490, 15070955944288, 185089043535730, 2287843817573898, 28440852786725695, 355345599519983962, 4459821165693379625, 56200963128262312342
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} binomial(2*n+3*k+1,k) * binomial(k,n-k)/(2*n+3*k+1).
PROG
(PARI) a(n) = sum(k=0, n, binomial(2*n+3*k+1, k)*binomial(k, n-k)/(2*n+3*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 25 2023
STATUS
approved