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%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
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