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.

1, 1, 4, 31, 351, 5144, 91816, 1918578, 45687682, 1216354021, 35689352250, 1141323078031, 39429988969021, 1461049507764175, 57720478019188989, 2419008380691088543, 107083662651332423339, 4988596265684542112304, 243781041304397011647766

Offset: 0

Author

Alois P. Heinz, Oct 26 2018

Keywords

• nonn

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..411

Crossrefs

Row sums of A256311.

Cf. A258498.

Programs

Maple

a:= n-> `if`(n=0, 1, add(add((-1)^i*(k-i)/n*add(binomial(3*n, j)
      *(n-j)*(k-i-1)^j, j=0..n-1)/(i!*(k-i)!), i=0..k), k=0..n)):
seq(a(n), n=0..20);