A248828 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.

1, 1, 3, 29, 523, 14289, 530526, 25066621, 1443039123, 98156060225, 7711583225338, 687676559089101, 68652814486950398, 7588068106131457489, 920064964125791788188, 121445943726500589053565, 17337678537189658091486851, 2661994674815094376005234945

Offset: 0

Author

Alois P. Heinz, Oct 15 2014

Keywords

• nonn

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Main diagonal of A183134.

Cf. A294491.

Programs

Maple

a:= n->`if`(n=0, 1, add(binomial(2*n, j)*(n-j)*(n-1)^j, j=0..n-1)/n):
seq(a(n), n = 0..20);

Mathematica

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 *)

Formula

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

a(n) ~ exp(-1) * 4^n * n^(n-5/2) / sqrt(Pi). - Vaclav Kotesovec, Oct 15 2014

a(n) = A294491(n) / n for n>0, a(0) = 1. - Alois P. Heinz, Oct 31 2017