A248828 - OEIS

%I #13 Oct 31 2017 23:06:38

%S 1,1,3,29,523,14289,530526,25066621,1443039123,98156060225,

%T 7711583225338,687676559089101,68652814486950398,7588068106131457489,

%U 920064964125791788188,121445943726500589053565,17337678537189658091486851,2661994674815094376005234945

%N Number of 2n-length words, either empty or beginning with the first character of an n-ary alphabet, that can be built by repeatedly inserting doublets into the initially empty word.

%H Alois P. Heinz, <a href="/A248828/b248828.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = A183134(n,n).

%F a(n) ~ exp(-1) * 4^n * n^(n-5/2) / sqrt(Pi). - _Vaclav Kotesovec_, Oct 15 2014

%F a(n) = A294491(n) / n for n>0, a(0) = 1. - _Alois P. Heinz_, Oct 31 2017

%e a(2) = 3: aaaa, aabb, abba (with alphabet {a,b}).

%p a:= n->`if`(n=0, 1, add(binomial(2*n, j)*(n-j)*(n-1)^j, j=0..n-1)/n):

%p seq(a(n), n = 0..20);

%t Flatten[{1,1,Table[Sum[Binomial[2*n, j]*(n-j)*(n-1)^j, {j,0,n-1}]/n,{n,2,20}]}] (* _Vaclav Kotesovec_, Oct 15 2014 *)

%Y Main diagonal of A183134.

%Y Cf. A294491.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Oct 15 2014