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

5,1

Links

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

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

Crossrefs

Column k=5 of A253180.

Sequence in context: A041841 A236270 A216703 * A187365 A294978 A180371

Adjacent sequences: A258390 A258391 A258392 * A258394 A258395 A258396

Keyword

nonn

Author

Alois P. Heinz, May 28 2015

Status

approved