A258395 - OEIS

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

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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