A258397 Number of 2n-length strings of balanced parentheses of exactly 9 different types that are introduced in ascending order.

4862, 755820, 67897830, 4633467300, 267074035800, 13733597077200, 650800305634050, 29021018652697500, 1235362166419751370, 50713478000403718500, 2022835296688063807950, 78843505678630977784500, 3016017325414346802772080, 113617986954086473298668800

Offset

9,1

Links

Alois P. Heinz, Table of n, a(n) for n = 9..650

Formula

Recurrence: (n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*n*(n+1)*a(n) = 90*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*n*(2*n - 1)*a(n-1) - 3480*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(2*n - 3)*(2*n - 1)*a(n-2) + 75600*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-3) - 1012368*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-4) + 8618400*(n-7)*(n-6)*(n-5)*(n-4)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-5) - 46315520*(n-7)*(n-6)*(n-5)*(2*n - 11)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-6) + 150105600*(n-7)*(n-6)*(2*n - 13)*(2*n - 11)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-7) - 262803456*(n-7)*(2*n - 15)*(2*n - 13)*(2*n - 11)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-8) + 185794560*(2*n - 17)*(2*n - 15)*(2*n - 13)*(2*n - 11)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-9). - Vaclav Kotesovec, Jun 01 2015

a(n) ~ 36^n / (9!*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015

Crossrefs

Column k=9 of A253180.

Sequence in context: A244106 A264182 A258496 * A215549 A295442 A227599

Adjacent sequences: A258394 A258395 A258396 * A258398 A258399 A258400

Keyword

nonn

Author

Alois P. Heinz, May 28 2015

Status

approved