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

Author

Alois P. Heinz, May 28 2015

Keywords

• nonn

Links

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

Crossrefs

Column k=6 of A253180.

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