A367258 G.f. satisfies A(x) = 1 + x*A(x) * (1 + x*A(x)^2)^2.

1, 1, 3, 10, 39, 162, 708, 3202, 14867, 70448, 339324, 1656443, 8176968, 40749277, 204727198, 1035837256, 5273360195, 26992906495, 138840628986, 717245323961, 3719765478096, 19359725932165, 101083353127371, 529341453000447, 2779470724644476, 14630696492685339

Offset: 0

Author

Seiichi Manyama, Nov 11 2023

Keywords

• nonn

Crossrefs

Cf. A000108.

Programs

PARI

a(n, s=2, t=1, u=2) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+1));

Formula

If g.f. satisfies A(x) = 1 + x*A(x)^t * (1 + x*A(x)^u)^s, then a(n) = Sum_{k=0..n} binomial(t*k+u*(n-k)+1,k) * binomial(s*k,n-k) / (t*k+u*(n-k)+1).