A258392 - OEIS

%I #7 Jun 01 2015 06:03:13

%S 14,420,8580,150150,2432430,37777740,572827580,8568059500,

%T 127199546012,1881416537000,27792098497800,410634370077750,

%U 6074408847920670,90017212151219100,1336818529866319500,19898794932394570500,296909055625560798420,4440849374395184751000

%N Number of 2n-length strings of balanced parentheses of exactly 4 different types that are introduced in ascending order.

%H Alois P. Heinz, <a href="/A258392/b258392.txt">Table of n, a(n) for n = 4..800</a>

%F Recurrence: (n-2)*(n-1)*n*(n+1)*a(n) = 20*(n-2)*(n-1)*n*(2*n - 1)*a(n-1) - 140*(n-2)*(n-1)*(2*n - 3)*(2*n - 1)*a(n-2) + 400*(n-2)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-3) - 384*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-4). - _Vaclav Kotesovec_, Jun 01 2015

%F a(n) ~ 16^n / (24*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Jun 01 2015

%Y Column k=4 of A253180.

%K nonn

%O 4,1

%A _Alois P. Heinz_, May 28 2015