cp's OEIS Frontend

A321033 Number of words of length 3n such that all letters of the ternary alphabet occur at least once and are introduced in ascending order and which can be built by repeatedly inserting triples into the initially empty word.

%I A321033 #6 Oct 26 2018 15:53:01
%S A321033 12,198,2520,29886,347907,4048966,47431488,560528820,6684500548,
%T A321033 80402461416,974694481735,11899112853684,146175947513247,
%U A321033 1805742311925206,22417900292210960,279556262002954608,3500139320096264886,43982137867266022438,554494988892196104240
%N A321033 Number of words of length 3n such that all letters of the ternary alphabet occur at least once and are introduced in ascending order and which can be built by repeatedly inserting triples into the initially empty word.
%H A321033 Alois P. Heinz, <a href="/A321033/b321033.txt">Table of n, a(n) for n = 3..889</a>
%p A321033 b:= (n, k)-> `if`(n=0, 1, k/n*add(binomial(3*n, j)*(n-j)*(k-1)^j, j=0..n-1)):
%p A321033 a:= n-> (k-> add((-1)^i*b(n, k-i)/(i!*(k-i)!), i=0..k))(3):
%p A321033 seq(a(n), n=3..25);
%Y A321033 Column k=3 of A256311.
%K A321033 nonn
%O A321033 3,1
%A A321033 _Alois P. Heinz_, Oct 26 2018