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

4,1

Links

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

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

Crossrefs

Column k=4 of A253180.

Sequence in context: A239785 A275025 A236156 * A269504 A033815 A187358

Adjacent sequences: A258389 A258390 A258391 * A258393 A258394 A258395

Keyword

nonn

Author

Alois P. Heinz, May 28 2015

Status

approved