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

0,3

Links

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

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

Example

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

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 *)

Crossrefs

Main diagonal of A183134.

Cf. A294491.

Sequence in context: A113871 A377832 A186451 * A210827 A092251 A304553

Adjacent sequences: A248825 A248826 A248827 * A248829 A248830 A248831

Keyword

nonn

Author

Alois P. Heinz, Oct 15 2014

Status

approved