A066211 - OEIS

%I #15 Jun 15 2018 20:51:56

%S 1,3,17,157,2081,36101,773665,19726085,582913217,19582414021,

%T 736891600001,30699450566885,1402556105125345,69719685409234277,

%U 3745929254826233441,216310377722912693701,13359435408855851031425,878701820865582786218885

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

%H Harry J. Smith, <a href="/A066211/b066211.txt">Table of n, a(n) for n = 0..100</a>

%F 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

%F a(n) ~ 2^(2*n+1/2) * n^n / exp(n). - _Vaclav Kotesovec_, Dec 29 2013

%t Table[Sum[(2*n)!/(2*n-j)!, {j, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Dec 29 2013 *)

%o (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

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Dec 17 2001