A258390 Number of 2n-length strings of balanced parentheses of exactly 2 different types that are introduced in ascending order.

2, 15, 98, 630, 4092, 27027, 181610, 1239810, 8582756, 60138078, 425800564, 3042175500, 21906338040, 158830645635, 1158564772890, 8496271312650, 62604582047700, 463275674416170, 3441483002640540, 25654715940496500, 191852749820189640, 1438895966711035950

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: A356554 A356578 A362768 * A027080 A208347 A293045

Adjacent sequences: A258387 A258388 A258389 * A258391 A258392 A258393

Keyword

nonn

Author

Alois P. Heinz, May 28 2015

Status

approved