A370479 G.f. satisfies A(x) = ( 1 + x * (A(x)^(1/2) / (1-x))^2 )^2.

1, 2, 9, 40, 184, 872, 4232, 20936, 105208, 535624, 2757000, 14324456, 75028152, 395750568, 2100380424, 11208429960, 60103977976, 323708642952, 1750294676744, 9497584905128, 51703651336888, 282302043458536, 1545558070957960, 8482843567140680

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

G.f.: B(x)^2 where B(x) is the g.f. of A006319.

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec((1+x*((1-x-sqrt(1-6*x+x^2))/(2*x))^2)^2)
(PARI) a(n, r=2, s=2, t=2, u=0) = 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. A045623, A370477.

Cf. A006319, A370480.

Sequence in context: A107979 A021001 A231134 * A038112 A268039 A367044

Adjacent sequences: A370476 A370477 A370478 * A370480 A370481 A370482

Keyword

nonn

Author

Seiichi Manyama, Mar 31 2024

Status

approved