A378952 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^2/(1 + x*A(x)^(4/3)) )^3.

1, 3, 18, 139, 1218, 11511, 114398, 1178421, 12469626, 134734092, 1480317468, 16487870031, 185744716414, 2112756042468, 24230663513604, 279889210974003, 3253295301115290, 38023971948455859, 446603044829013514, 5268557500949993964, 62398899992129490756

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)^(5/3)/(1 + x*A(x)^(4/3)) )^3.

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

(3) A(x) = B(x)^3 where B(x) is the g.f. of A364765.

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=6, 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. A371724, A378951.

Cf. A364765, A378954.

Cf. A378891.

Sequence in context: A357403 A039618 A183363 * A216492 A127129 A186266

Adjacent sequences: A378945 A378946 A378951 * A378953 A378954 A378957

Keyword

nonn,new

Author

Seiichi Manyama, Dec 11 2024

Status

approved