%I #16 Dec 02 2023 11:46:41
%S 0,6,240,12600,846720,69854400,6849722880,779155977600,
%T 100919250432000,14668613050291200,2364758225077248000,
%U 418798681661180620800,80831074222717378560000,16887920864389166592000000,3797443866983262444748800000,914438045469094536918528000000
%N a(n) = binomial(2*n, n - 1)*(2*n + 1)! / n!.
%F a(n) = A271703(2*n + 1, n).
%F a(n) = binomial(2*n+1,n)*(2n)!/(n-1)! for n > 0. - _Chai Wah Wu_, Nov 30 2023
%F a(n) = n*A000108(n)*(2*n + 1)!/n!. - _Detlef Meya_, Dec 02 2023
%p seq(binomial(2*n, n - 1)*(2*n + 1)! / n!, n = 0..15);
%t a[n_]:=n*CatalanNumber[n]*Gamma[2*n+2]/n!;Flatten[Table[a[n],{n,0,15}]] (* _Detlef Meya_, Dec 02 2023 *)
%Y Cf. A000108 (Catalan), A271703.
%K nonn
%O 0,2
%A _Peter Luschny_, Nov 29 2023