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

3,1

Links

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

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

Crossrefs

Column k=3 of A253180.

Sequence in context: A359110 A187587 A006471 * A061628 A193369 A111911

Adjacent sequences: A258388 A258389 A258390 * A258392 A258393 A258394

Keyword

nonn

Author

Alois P. Heinz, May 28 2015

Status

approved