A378670 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^(3/2)/(1 - x*A(x)^(3/2)) )^2.

1, 2, 11, 78, 627, 5432, 49464, 466726, 4522871, 44747874, 450127999, 4589821576, 47333631828, 492836382192, 5173697858508, 54700317431958, 581946708333055, 6225343630256678, 66921440314606905, 722546760572660030, 7832054418695360555, 85198490262065775840

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

G.f.: exp( 2/3 * Sum_{k>=1} A378612(k) * x^k/k ).

G.f.: B(x)^2 where B(x) is the g.f. of A243659.

a(n) = 2 * Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(n,k) * binomial(3*n+k+2,n)/(3*n+k+2).

a(n) = 2 * Sum_{k=0..n} binomial(3*n+k+2,k) * binomial(n-1,n-k)/(3*n+k+2).

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

Prog

(PARI) a(n) = 2*sum(k=0, n, 2^k*(-1)^(n-k)*binomial(n, k)*binomial(3*n+k+2, n)/(3*n+k+2));
(PARI) a(n, r=2, s=1, t=4, u=3) = 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. A243659, A369012.

Cf. A010683, A211789, A378668.

Cf. A378612.

Sequence in context: A369542 A079266 A094569 * A151418 A154273 A253256

Adjacent sequences: A378666 A378668 A378669 * A378672 A378673 A378676

Keyword

nonn,new

Author

Seiichi Manyama, Dec 02 2024

Status

approved