A258394 Number of 2n-length strings of balanced parentheses of exactly 6 different types that are introduced in ascending order.

132, 9009, 380380, 12864852, 383402292, 10551322782, 275335499824, 6924802684800, 169656773406120, 4078556074277685, 96700630711999860, 2269529269318731420, 52868514692841609300, 1224857602490265215010, 28265620407321158141280, 650452332645092821924080

Offset

6,1

Links

Alois P. Heinz, Table of n, a(n) for n = 6..700

Formula

Recurrence: (n-4)*(n-3)*(n-2)*(n-1)*n*(n+1)*a(n) = 42*(n-4)*(n-3)*(n-2)*(n-1)*n*(2*n - 1)*a(n-1) - 700*(n-4)*(n-3)*(n-2)*(n-1)*(2*n - 3)*(2*n - 1)*a(n-2) + 5880*(n-4)*(n-3)*(n-2)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-3) - 25984*(n-4)*(n-3)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-4) + 56448*(n-4)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-5) - 46080*(2*n - 11)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-6). - Vaclav Kotesovec, Jun 01 2015

a(n) ~ 24^n / (720*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015

Crossrefs

Column k=6 of A253180.

Sequence in context: A258493 A184893 A035818 * A215546 A269042 A216787

Adjacent sequences: A258391 A258392 A258393 * A258395 A258396 A258397

Keyword

nonn

Author

Alois P. Heinz, May 28 2015

Status

approved