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%I #10 Oct 23 2015 12:21:33
%S 1,1,19,469,13123,395461,12517939,410380885,13811907043,474457464613,
%T 16567069507219,586287339402997,20980966876537411,757961579781924805,
%U 27605221102084999411,1012488016842242735509,37364825362229946450595,1386427393386051832383589
%N Number of 3n-length 7-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.
%H Alois P. Heinz, <a href="/A218477/b218477.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = 1/n * Sum_{j=0..n-1} C(3*n,j)*(n-j)*6^j for n>0, a(0) = 1.
%F Recurrence: n*(2*n-1)*(5*n-6)*a(n) = (3835*n^3 - 7127*n^2 + 3201*n - 180)*a(n-1) - 3087*(3*n-5)*(3*n-4)*(5*n-1)*a(n-2). - _Vaclav Kotesovec_, Aug 31 2014
%F a(n) ~ 3^(4*n+3/2) / (121 * 2^(n-1) * sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Aug 31 2014
%p a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*6^j, j=0..n-1)/n):
%p seq(a(n), n=0..20);
%Y Column k=7 of A213027.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Oct 29 2012
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