A364625 G.f. satisfies A(x) = 1/(1-x)^3 + x^2*A(x)^2.

1, 3, 7, 16, 38, 95, 249, 678, 1901, 5451, 15906, 47066, 140868, 425657, 1296665, 3977684, 12276617, 38094013, 118768915, 371875752, 1168843808, 3686549845, 11664123048, 37011249678, 117750111763, 375529083267, 1200327617200, 3844662925222, 12338289374046

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Formula

G.f.: A(x) = 2 / ( (1-x)^3 * (1 + sqrt( 1 - 4*x^2/(1-x)^3 )) ).

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(2/((1-x)^3*(1+sqrt(1-4*x^2/(1-x)^3))))

Crossrefs

Cf. A000108, A086615, A162481, A360045.

Cf. A364626, A364627.

Sequence in context: A323225 A293065 A211278 * A196154 A227235 A304937

Adjacent sequences: A364622 A364623 A364624 * A364626 A364627 A364628

Keyword

nonn

Author

Seiichi Manyama, Jul 30 2023

Status

approved