A367282 G.f. satisfies A(x) = 1 + x*A(x)^2 * (1 + x*A(x)^2)^2.

1, 1, 4, 18, 94, 527, 3108, 18993, 119214, 763997, 4978304, 32883853, 219690066, 1481858835, 10078051830, 69030877581, 475795428158, 3297527987794, 22965847261928, 160649189379029, 1128201207643744, 7951399289858530, 56222323349767666

Offset

0,3

Links

Table of n, a(n) for n=0..22.

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=2, 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. A002293, A073155, A214372, A367283.

Cf. A000108, A367258.

Cf. A367237.

Sequence in context: A346763 A121584 A209256 * A364475 A059227 A259533

Adjacent sequences: A367279 A367280 A367281 * A367283 A367284 A367285

Keyword

nonn

Author

Seiichi Manyama, Nov 12 2023

Status

approved