A240530 a(n) = 4*(2*n)! / (n!)^2.

4, 8, 24, 80, 280, 1008, 3696, 13728, 51480, 194480, 739024, 2821728, 10816624, 41602400, 160466400, 620470080, 2404321560, 9334424880, 36300541200, 141381055200, 551386115280, 2153031497760, 8416395854880, 32933722910400, 128990414732400

Offset: 0

Author

Vincenzo Librandi, Apr 12 2014

Keywords

• nonn

Comments

Apart from first term, the same as A146534. - Arkadiusz Wesolowski, Apr 12 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• M. Pedrazzi and G. Goldoni, Un labirinto cartesiano (A Cartesian Labyrinth), Archimede, Anno XXXVIII, Jan-Mar 1986, p. 41 (in Italian).

Crossrefs

Cf. A000984, A028329, A146534.

Programs

GAP

List([0..30], n-> 4*Binomial(2*n,n) ); # G. C. Greubel, Dec 19 2019

Magma

[4*Binomial (2*n,n): n in [0..30]];

Maple

seq( 4*binomial(2*n,n), n=0..30); # G. C. Greubel, Dec 19 2019

Mathematica

Table[4*(2*n)!/(n!)^2, {n, 0, 40}] (* or *) CoefficientList[Series[4/Sqrt[1 - 4 x], {x, 0, 50}], x]

PARI

vector(31, n, 4*binomial(2*n-2, n-1)) \\ G. C. Greubel, Dec 19 2019

Sage

[4*binomial(2*n,n) for n in (0..30)] # G. C. Greubel, Dec 19 2019

Formula

G.f.: 4/sqrt(1-4*x).

a(n) = 4*binomial(2*n, n) = 4*A000984(n) = 2*A028329(n).

D-finite with recurrence: n*a(n) - 2*(2*n-1)*a(n-1) = 0 for n > 0.