A258396 - OEIS

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A258396

Number of 2n-length strings of balanced parentheses of exactly 8 different types that are introduced in ascending order.

1430, 175032, 12597000, 698377680, 33079524324, 1411221754800, 55928745100800, 2100173331484800, 75727786603836510, 2646827388046104120, 90290940344491887000, 3021580012515765901200, 99583828881536195805180, 3242049884573075122369680

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OFFSET

8,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 8..650

FORMULA

Recurrence: (n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*n*(n+1)*a(n) = 72*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*n*(2*n - 1)*a(n-1) - 2184*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(2*n - 3)*(2*n - 1)*a(n-2) + 36288*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-3) - 359184*(n-6)*(n-5)*(n-4)*(n-3)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-4) + 2153088*(n-6)*(n-5)*(n-4)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-5) - 7559936*(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) + 14026752*(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) - 10321920*(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). - Vaclav Kotesovec, Jun 01 2015

a(n) ~ 32^n / (8!*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015

CROSSREFS

Column k=8 of A253180.

Sequence in context: A264181 A064305 A258495 * A215548 A274253 A227598

Adjacent sequences: A258393 A258394 A258395 * A258397 A258398 A258399

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 28 2015

STATUS

approved