A371579 G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) * (1 + x*A(x))^2 )^2.

1, 2, 15, 134, 1367, 15032, 173836, 2083806, 25660383, 322666882, 4125822703, 53482104104, 701223274308, 9283066366256, 123912439591104, 1665895096499278, 22537232138264271, 306586712969384678, 4191205834907493725, 57548344232637695030, 793311718924341065567

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=5, u=2) = 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. A371574.

Sequence in context: A140306 A143924 A217483 * A214043 A347993 A215922

Adjacent sequences: A371576 A371577 A371578 * A371580 A371581 A371582

Keyword

nonn

Author

Seiichi Manyama, Mar 28 2024

Status

approved