OFFSET
0,3
COMMENTS
Also the number of rooted closed walks of length 2n on the infinite rooted n-ary tree.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..322
FORMULA
EXAMPLE
a(2) = 6 because 6 words of length 4 can be built over 2-letter alphabet {a, b} by repeatedly inserting doublets (words with two equal letters) into the initially empty word: aaaa, aabb, abba, baab, bbaa, bbbb.
MAPLE
a:= n-> `if`(n=0, 1, add(binomial(2*n, j)*(n-j)*(n-1)^j, j=0..n-1)):
seq(a(n), n=0..21);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 31 2017
STATUS
approved