A258393 Number of 2n-length strings of balanced parentheses of exactly 5 different types that are introduced in ascending order.

42, 1980, 60060, 1501500, 33795762, 714249900, 14504269780, 286931752800, 5578065392900, 107178276605400, 2043352620527400, 38758743724018500, 732849800716048290, 13831507110589591500, 260829110106412824900, 4917878997439418010000, 92758042341429880435020

Offset: 5

Author

Alois P. Heinz, May 28 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..750

Crossrefs

Column k=5 of A253180.

Formula

Recurrence: (n-3)*(n-2)*(n-1)*n*(n+1)*a(n) = 30*(n-3)*(n-2)*(n-1)*n*(2*n - 1)*a(n-1) - 340*(n-3)*(n-2)*(n-1)*(2*n - 3)*(2*n - 1)*a(n-2) + 1800*(n-3)*(n-2)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-3) - 4384*(n-3)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-4) + 3840*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-5). - Vaclav Kotesovec, Jun 01 2015

a(n) ~ 20^n / (120*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015