A258397 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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