A370477 G.f. satisfies A(x) = ( 1 + x * (A(x)^(1/2) / (1-x))^(3/2) )^2.

1, 2, 7, 24, 83, 290, 1023, 3640, 13052, 47124, 171190, 625328, 2295561, 8464690, 31339455, 116458200, 434217000, 1623971580, 6090823890, 22903571280, 86332453350, 326145976884, 1234662753126, 4682968975664, 17794062340008, 67726620644200

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

G.f.: B(x)^2 where B(x) is the g.f. of A071724.

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec((1+x*((1-sqrt(1-4*x))/(2*x))^3)^2)
(PARI) a(n, r=2, s=3/2, t=3/2, 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, A370479.

Cf. A071724, A370478.

Sequence in context: A020727 A003480 A329274 * A088854 A000777 A369266

Adjacent sequences: A370474 A370475 A370476 * A370478 A370479 A370480

Keyword

nonn

Author

Seiichi Manyama, Mar 31 2024

Status

approved