A378801 G.f. A(x) satisfies A(x) = ( 1 + x/(1 - x*A(x)^(2/3)) )^3.

1, 3, 6, 16, 48, 153, 511, 1761, 6219, 22383, 81804, 302766, 1132475, 4274166, 16256685, 62249167, 239772510, 928398831, 3611539758, 14107963848, 55318781982, 217652858539, 859027927911, 3400055112777, 13492710661658, 53673238384560, 213984657134418

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Formula

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

G.f.: A(x) = (1 + x*B(x))^3 where B(x) is the g.f. of A161634.

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(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r).

Prog

(PARI) a(n, r=3, s=1, t=0, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A161634, A365118.

Cf. A005554, A378858.

Sequence in context: A369073 A300355 A360865 * A274294 A201969 A367639

Adjacent sequences: A378798 A378799 A378800 * A378802 A378803 A378804

Keyword

nonn

Author

Seiichi Manyama, Dec 09 2024

Status

approved