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A258391 Number of 2n-length strings of balanced parentheses of exactly 3 different types that are introduced in ascending order. 2
5, 84, 1050, 11880, 129129, 1381380, 14707550, 156706680, 1675459786, 17998446312, 194361212500, 2110052926800, 23026236054345, 252513376831620, 2781895215981750, 30778564965687000, 341873708072702190, 3811170628172227320, 42628644369844747500 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..900

FORMULA

Recurrence: (n-1)*n*(n+1)*a(n) = 12*(n-1)*n*(2*n - 1)*a(n-1) - 44*(n-1)*(2*n - 3)*(2*n - 1)*a(n-2) + 48*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-3). - Vaclav Kotesovec, Jun 01 2015

a(n) ~ 12^n / (6*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015

CROSSREFS

Column k=3 of A253180.

Sequence in context: A271219 A187587 A006471 * A061628 A193369 A111911

Adjacent sequences:  A258388 A258389 A258390 * A258392 A258393 A258394

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 28 2015

STATUS

approved

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Last modified April 14 07:59 EDT 2021. Contains 342946 sequences. (Running on oeis4.)