A258395 Number of 2n-length strings of balanced parentheses of exactly 7 different types that are introduced in ascending order.

429, 40040, 2246244, 98760480, 3761539782, 130505896752, 4245988489600, 131928199603200, 3962683868528385, 116039722090972680, 3332921846278964940, 94315723869947580000, 2638390752595156276410, 73147630662437905413840, 2013841857892713303414960

Offset

7,1

Links

Alois P. Heinz, Table of n, a(n) for n = 7..650

Formula

Recurrence: (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*n*(n+1)*a(n) = 56*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*n*(2*n - 1)*a(n-1) - 1288*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(2*n - 3)*(2*n - 1)*a(n-2) + 15680*(n-5)*(n-4)*(n-3)*(n-2)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-3) - 108304*(n-5)*(n-4)*(n-3)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-4) + 420224*(n-5)*(n-4)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-5) - 836352*(n-5)*(2*n - 11)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-6) + 645120*(2*n - 13)*(2*n - 11)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-7). - Vaclav Kotesovec, Jun 01 2015

a(n) ~ 28^n / (7!*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015

Crossrefs

Column k=7 of A253180.

Sequence in context: A264180 A270412 A258494 * A215547 A181195 A227597

Adjacent sequences: A258392 A258393 A258394 * A258396 A258397 A258398

Keyword

nonn

Author

Alois P. Heinz, May 28 2015

Status

approved