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

0,2

Links

Table of n, a(n) for n=0..15.

Formula

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

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

a(n) ~ 2^(4*n+3/2) * n^(n+1/2) / (exp(n) * sqrt(Pi)). - Amiram Eldar, Sep 18 2025

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!; Table[a[n], {n, 0, 15}] (* Detlef Meya, Dec 02 2023 *)

Crossrefs

Cf. A000108 (Catalan), A271703.

Sequence in context: A002022 A378778 A065948 * A052510 A234633 A137892

Adjacent sequences: A367773 A367774 A367775 * A367777 A367778 A367779

Keyword

nonn,easy

Author

Peter Luschny, Nov 29 2023

Status

approved