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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. 3
1, 1, 3, 29, 523, 14289, 530526, 25066621, 1443039123, 98156060225, 7711583225338, 687676559089101, 68652814486950398, 7588068106131457489, 920064964125791788188, 121445943726500589053565, 17337678537189658091486851, 2661994674815094376005234945 (list; graph; refs; listen; history; text; internal format)
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: A302923 A113871 A186451 * A210827 A092251 A304553

Adjacent sequences:  A248825 A248826 A248827 * A248829 A248830 A248831

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 15 2014

STATUS

approved

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Last modified February 19 07:51 EST 2019. Contains 320309 sequences. (Running on oeis4.)