A066211 a(n) = Sum_{j=0..n} (2*n)!/(2*n-j)!.

1, 3, 17, 157, 2081, 36101, 773665, 19726085, 582913217, 19582414021, 736891600001, 30699450566885, 1402556105125345, 69719685409234277, 3745929254826233441, 216310377722912693701, 13359435408855851031425, 878701820865582786218885

Offset: 0

Author

N. J. A. Sloane, Dec 17 2001

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 0..100

Programs

Mathematica

Table[Sum[(2*n)!/(2*n-j)!, {j, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Dec 29 2013 *)

PARI

{ for (n=0, 100, s=0; for (j=0, n, s+=(2*n)!/(2*n - j)!); write("b066211.txt", n, " ", s) ) } \\ Harry J. Smith, Feb 06 2010

Formula

Recurrence: (8*n^3 - 34*n^2 + 47*n - 20)*a(n) = (32*n^5 - 120*n^4 + 144*n^3 - 56*n^2 + 7*n + 2)*a(n-1) - 2*(2*n-3)*(32*n^5 - 144*n^4 + 238*n^3 - 161*n^2 + 38*n - 1)*a(n-2) + 4*(n-2)*(2*n-5)*(2*n-3)*(8*n^3 - 10*n^2 + 3*n + 1)*a(n-3). - Vaclav Kotesovec, Dec 29 2013

a(n) ~ 2^(2*n+1/2) * n^n / exp(n). - Vaclav Kotesovec, Dec 29 2013