A367285 G.f. satisfies A(x) = 1 + x*A(x)^2 * (1 + x*A(x)^2)^3.

1, 1, 5, 26, 159, 1042, 7185, 51340, 376806, 2823734, 21516113, 166196703, 1298413089, 10241803340, 81454834164, 652465062453, 5259084437170, 42624217133130, 347160390473763, 2839928983316595, 23323730673818467, 192237734035157372, 1589602164422747636

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=3, 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. A360076, A361305.

Cf. A137953, A367261.

Cf. A367240.

Sequence in context: A001705 A185108 A302442 * A349882 A209672 A367041

Adjacent sequences: A367282 A367283 A367284 * A367286 A367287 A367288

Keyword

nonn

Author

Seiichi Manyama, Nov 12 2023

Status

approved