A258391 Number of 2n-length strings of balanced parentheses of exactly 3 different types that are introduced in ascending order.

5, 84, 1050, 11880, 129129, 1381380, 14707550, 156706680, 1675459786, 17998446312, 194361212500, 2110052926800, 23026236054345, 252513376831620, 2781895215981750, 30778564965687000, 341873708072702190, 3811170628172227320, 42628644369844747500

Offset: 3

Author

Alois P. Heinz, May 28 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..900

Crossrefs

Column k=3 of A253180.

Formula

Recurrence: (n-1)*n*(n+1)*a(n) = 12*(n-1)*n*(2*n - 1)*a(n-1) - 44*(n-1)*(2*n - 3)*(2*n - 1)*a(n-2) + 48*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-3). - Vaclav Kotesovec, Jun 01 2015

a(n) ~ 12^n / (6*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015