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A258390 Number of 2n-length strings of balanced parentheses of exactly 2 different types that are introduced in ascending order. 2
2, 15, 98, 630, 4092, 27027, 181610, 1239810, 8582756, 60138078, 425800564, 3042175500, 21906338040, 158830645635, 1158564772890, 8496271312650, 62604582047700, 463275674416170, 3441483002640540, 25654715940496500, 191852749820189640, 1438895966711035950 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..1000

FORMULA

a(n) = (2*n-1)*(6*n*a(n-1)-8*(2*n-3)*a(n-2))/(n*(n+1)) for n>2, a(2)=2, a(n)=0 for n<2.

a(n) = (2^(n-1)-1) * binomial(2n,n)/(n+1) = (2^(n-1)-1)*A000108(n). - Vaclav Kotesovec, Jun 01 2015

MAPLE

a:= proc(n) option remember; `if`(n<3, [0$2, 2][n+1],

      (2*n-1)*(6*n*a(n-1) -8*(2*n-3)*a(n-2))/(n*(n+1)))

    end:

seq(a(n), n=2..25);

MATHEMATICA

Table[(2^(n-1)-1)*Binomial[2n, n]/(n+1), {n, 2, 20}] (* Vaclav Kotesovec, Jun 01 2015 *)

CROSSREFS

Column k=2 of A253180.

Sequence in context: A037753 A037641 A288952 * A027080 A208347 A293045

Adjacent sequences:  A258387 A258388 A258389 * A258391 A258392 A258393

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 28 2015

STATUS

approved

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Last modified June 17 18:47 EDT 2021. Contains 345085 sequences. (Running on oeis4.)