A202689 a(n) = (2n)! * (n+1)! / 2^(2n).

1, 1, 9, 270, 18900, 2551500, 589396500, 214540326000, 115851776040000, 88626608670600000, 92614806060777000000, 128364121200236922000000, 230285233433225038068000000, 523898906060586961604700000000, 1485253398681764036149324500000000

Offset: 0

Author

Alexander R. Povolotsky, Dec 22 2011

Keywords

• nonn
• easy

Comments

a(n) is always an integer since a(n+1)/a(n) = n^3 + 7/2*n^2 + 7/2*n + 1 which is always an integer. [D. S. McNeil, Dec 22 2011]

To further follow the above comment from D. S. McNeil: a(n+1)/a(n) is given in A002414. [Alexander R. Povolotsky, Dec 23 2011]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• T. Piezas, Notes and conjectures on properties of polynomials, arising in "Construction Of Binomial Sums For π And Polylogarithmic Constants Inspired by BBP Formulas" (by Boris Gourévitch, Jesús Guillera Goyanes) and also relevant to further unpublished follow-up work by J. Cullen, T. Piezas, J. Guillera, and B. Gourevitch.
• Index to divisibility sequences

Crossrefs

Cf. A002414.

Programs

Magma

[Factorial(2*n)*Factorial(n+1)/2^(2*n): n in [0..15]]; // Vincenzo Librandi, Feb 09 2012

Mathematica

Table[(2n)!(n+1)!/2^(2n),{n,0,20}] (* Vincenzo Librandi, Feb 09 2012 *)

PARI

a(n)=(2*n)!*(n+1)!>>(2*n) \\ Charles R Greathouse IV, Dec 23 2011

Formula

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

a(n+1) = a(n)*(n^3 + 7/2*n^2 + 7/2*n + 1).

a(n+1) = a(n)*A002414(n+1) for n >= 0.