A378951 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(5/3)/(1 + x*A(x)) )^3.

1, 3, 15, 94, 663, 5025, 39970, 329145, 2782095, 23999078, 210427869, 1869908364, 16802935370, 152425394958, 1393972037301, 12838326815582, 118970843349711, 1108503805898190, 10378559702646846, 97593299922016224, 921294705307189029

Offset

0,2

Links

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

Formula

G.f. A(x) satisfies:

(1) A(x) = 1/( 1 - x*A(x)^(4/3)/(1 + x*A(x)) )^3.

(2) A(x) = 1 + x * A(x) * (1 + A(x)^(2/3) + A(x)^(4/3)).

(3) A(x) = B(x)^3 where B(x) is the g.f. of A271469.

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=3, s=-1, t=5, u=3) = 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. A371724, A378952.

Cf. A271469, A370474.

Cf. A378891.

Sequence in context: A369301 A368964 A274734 * A177341 A220262 A365560

Adjacent sequences: A378942 A378945 A378946 * A378952 A378953 A378954

Keyword

nonn,new

Author

Seiichi Manyama, Dec 11 2024

Status

approved