A152029 a(n) = 2^n*(2*n)!/((n+1)!).

1, 2, 16, 240, 5376, 161280, 6082560, 276756480, 14760345600, 903333150720, 62412108595200, 4805732361830400, 408117579035443200, 37896632339005440000, 3819980539771748352000, 415422883700177633280000, 48482294191832495554560000, 6044126009248451112468480000

Offset: 0

Author

N. J. A. Sloane, Sep 15 2009

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..334
• K. Casteels and B. Stevens, Universal cycles of (n-1)-partitions of an n-set, Discr. Math., 309 (2009), 5332-5340.

Programs

Magma

[2^n*Factorial(2*n)/Factorial(n+1): n in [0..20]]; // Vincenzo Librandi, Jan 27 2017

Maple

seq(2^n*(2*n)!/(n+1)!,n=0..40); # Robert Israel, Jan 25 2017

Mathematica

Table[(2^n) (2 n)! / (n + 1)!, {n, 0, 20}] (* Vincenzo Librandi, Jan 27 2017 *)
With[{nn=20},CoefficientList[Series[2/(1+(1-8x)^(1/2)),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 11 2023 *)

PARI

a(n) = 2^n*(2*n)!/(n+1)! \\ Michel Marcus, Jun 02 2013

Formula

E.g.f 2/(1+(1-8*x)^(1/2)). - Sergei N. Gladkovskii, Oct 26 2012

a(n) = 2^n * A001761(n) = A065140(n)/(n+1)!. - Michel Marcus, Jun 02 2013

G.f.: G(0)/2, where G(k)= 1 + 1/(1 - 2*x/(2*x + (k+2)/((2*k+1)*(2*k+2))/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 03 2013

4*(n+1)*(2*n+1)*a(n) = (n+2)*a(n+1). - Robert Israel, Jan 25 2017

E.g.f.: 1/(1 - 2*x/(1 - 2*x/(1 - 2*x/(1 - 2*x/(1 - 2*x/(1 - ...)))))), a continued fraction. - Ilya Gutkovskiy, May 10 2017