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

0,3

Links

Table of n, a(n) for n=0..25.

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).

Prog

(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));

Crossrefs

Cf. A000108.

Sequence in context: A218001 A307490 A253194 * A338185 A151072 A151073

Adjacent sequences: A367255 A367256 A367257 * A367259 A367260 A367261

Keyword

nonn

Author

Seiichi Manyama, Nov 11 2023

Status

approved