A258392 Number of 2n-length strings of balanced parentheses of exactly 4 different types that are introduced in ascending order.

14, 420, 8580, 150150, 2432430, 37777740, 572827580, 8568059500, 127199546012, 1881416537000, 27792098497800, 410634370077750, 6074408847920670, 90017212151219100, 1336818529866319500, 19898794932394570500, 296909055625560798420, 4440849374395184751000

Offset: 4

Author

Alois P. Heinz, May 28 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..800

Crossrefs

Column k=4 of A253180.

Formula

Recurrence: (n-2)*(n-1)*n*(n+1)*a(n) = 20*(n-2)*(n-1)*n*(2*n - 1)*a(n-1) - 140*(n-2)*(n-1)*(2*n - 3)*(2*n - 1)*a(n-2) + 400*(n-2)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-3) - 384*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-4). - Vaclav Kotesovec, Jun 01 2015

a(n) ~ 16^n / (24*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015