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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
1, 1, 4, 31, 351, 5144, 91816, 1918578, 45687682, 1216354021, 35689352250, 1141323078031, 39429988969021, 1461049507764175, 57720478019188989, 2419008380691088543, 107083662651332423339, 4988596265684542112304, 243781041304397011647766 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 24 10:03 EDT 2021. Contains 348225 sequences. (Running on oeis4.)