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A321031 Number of words of length 3n such that the index set of occurring letters is {1, 2, ..., k}, all letters are introduced in ascending order, and the words can be built by repeatedly inserting triples into the initially empty word. 3

%I

%S 1,1,4,31,351,5144,91816,1918578,45687682,1216354021,35689352250,

%T 1141323078031,39429988969021,1461049507764175,57720478019188989,

%U 2419008380691088543,107083662651332423339,4988596265684542112304,243781041304397011647766

%N Number of words of length 3n such that the index set of occurring letters is {1, 2, ..., k}, all letters are introduced in ascending order, and the words can be built by repeatedly inserting triples into the initially empty word.

%H Alois P. Heinz, <a href="/A321031/b321031.txt">Table of n, a(n) for n = 0..411</a>

%e a(2) = 4: aaaaaa, aaabbb, aabbba, abbbaa.

%p a:= n-> `if`(n=0, 1, add(add((-1)^i*(k-i)/n*add(binomial(3*n, j)

%p *(n-j)*(k-i-1)^j, j=0..n-1)/(i!*(k-i)!), i=0..k), k=0..n)):

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

%Y Row sums of A256311.

%Y Cf. A258498.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Oct 26 2018

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Last modified December 6 22:42 EST 2021. Contains 349567 sequences. (Running on oeis4.)