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

0,3

Links

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

Example

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

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);

Crossrefs

Row sums of A256311.

Cf. A258498.

Sequence in context: A145160 A129271 A136728 * A102757 A295254 A343832

Adjacent sequences: A321028 A321029 A321030 * A321032 A321033 A321034

Keyword

nonn

Author

Alois P. Heinz, Oct 26 2018

Status

approved