|
%I #7 Jan 25 2023 09:13:20
%S 1,6,210,13860,1351350,174594420,28109701620,5421156741000,
%T 1218404977539750,312723944235202500,90252130306279441500,
%U 28929910132721937339000,10197793321784482911997500,3920659309406065045704885000,1632674555274097086889962825000,732091270584905133761459330730000
%N a(n) = binomial(4*n, 2*n)*(2*n)!/(2^n*n!).
%F a(n) = (2^(3*n)*Gamma(2*n + 1/2))/(sqrt(Pi)*Gamma(n + 1)).
%F a(n) = A359760(4*n, 2*n), the central terms of the triangle without the zeros.
%F a(n) = A001448(n)*A001147(n). - _R. J. Mathar_, Jan 25 2023
%F D-finite with recurrence n*a(n) -2*(4*n-1)*(4*n-3)*a(n-1)=0. - _R. J. Mathar_, Jan 25 2023
%p a := binomial(4*n, 2*n)*(2*n)!/(2^n*n!):
%p seq(a(n), n = 0..15);
%Y Cf. A359760.
%K nonn,easy
%O 0,2
%A _Peter Luschny_, Jan 14 2023
|
