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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. 2
1, 1, 4, 61, 1810, 82593, 5153626, 410380885, 39868799482, 4579454148865, 607729841261560, 91553310170011501, 15441283593044256696, 2883254656878648757729, 590578881927993264483880, 131681888589427990097216549, 31753512197914767223878851626 (list; graph; refs; listen; history; text; internal format)
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

Diagonal of A213027.

Sequence in context: A229666 A252973 A262654 * A304176 A326225 A102193

Adjacent sequences:  A218469 A218470 A218471 * A218473 A218474 A218475

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 29 2012

STATUS

approved

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Last modified October 17 07:39 EDT 2021. Contains 348048 sequences. (Running on oeis4.)