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A218472

Number of 3n-length n-ary words, either empty or beginning with the first letter of the alphabet, that can be built by repeatedly inserting triples of identical letters into the initially empty word.

1, 1, 4, 61, 1810, 82593, 5153626, 410380885, 39868799482, 4579454148865, 607729841261560, 91553310170011501, 15441283593044256696, 2883254656878648757729, 590578881927993264483880, 131681888589427990097216549, 31753512197914767223878851626

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OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..150

FORMULA

a(n) = 1/n * Sum_{j=0..n-1} C(3*n,j)*(n-j)*(n-1)^j for n>1, a(n) = 1 else.

a(n) ~ 3^(3*n + 1/2) * n^(n - 5/2) / (sqrt(Pi) * exp(1) * 2^(2*n+2)). - Vaclav Kotesovec, Mar 25 2016

MAPLE

a:= n-> `if`(n<2, 1, add(binomial(3*n, j)*(n-j)*(n-1)^j, j=0..n-1)/n):

seq(a(n), n=0..20);

CROSSREFS