A371586 G.f. satisfies A(x) = ( 1 + x*A(x)^2 * (1 + x*A(x)^2)^2 )^2.

1, 2, 13, 106, 986, 9898, 104535, 1144630, 12876908, 147937396, 1728352171, 20471245898, 245254954252, 2966792716710, 36186910210761, 444559817944096, 5495828249436652, 68318636646858588, 853455362282694440, 10708603125245767280, 134897492549870974674

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

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

Prog

(PARI) a(n, r=2, s=2, t=4, u=4) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A367282.

Sequence in context: A371583 A083062 A204261 * A371574 A127746 A199124

Adjacent sequences: A371583 A371584 A371585 * A371587 A371588 A371589

Keyword

nonn

Author

Seiichi Manyama, Mar 28 2024

Status

approved