A367776 a(n) = binomial(2*n, n - 1)*(2*n + 1)! / n!.

0, 6, 240, 12600, 846720, 69854400, 6849722880, 779155977600, 100919250432000, 14668613050291200, 2364758225077248000, 418798681661180620800, 80831074222717378560000, 16887920864389166592000000, 3797443866983262444748800000, 914438045469094536918528000000

Offset: 0

Author

Peter Luschny, Nov 29 2023

Keywords

• nonn

Crossrefs

Cf. A000108 (Catalan), A271703.

Programs

Maple

seq(binomial(2*n, n - 1)*(2*n + 1)! / n!, n = 0..15);

Mathematica

a[n_]:=n*CatalanNumber[n]*Gamma[2*n+2]/n!;Flatten[Table[a[n],{n,0,15}]] (* Detlef Meya, Dec 02 2023 *)

Formula

a(n) = A271703(2*n + 1, n).

a(n) = binomial(2*n+1,n)*(2n)!/(n-1)! for n > 0. - Chai Wah Wu, Nov 30 2023

a(n) = n*A000108(n)*(2*n + 1)!/n!. - Detlef Meya, Dec 02 2023