A291057 Cardinality of the smallest nonempty class of length minimal languages with exactly n nonempty words each over a countably infinite alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

1, 1, 2, 1, 4, 6, 4, 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 26, 325, 2600, 14950, 65780, 230230, 657800, 1562275, 3124550, 5311735, 7726160, 9657700, 10400600, 9657700, 7726160, 5311735, 3124550, 1562275, 657800, 230230, 65780, 14950, 2600, 325, 26, 1

Offset: 0

Author

Alois P. Heinz, Oct 20 2017

Keywords

• nonn
• look

Comments

a(n) is the smallest nonzero term in column n of A293815.

Examples

			a(0) = 1: {{}}.
a(1) = 1: {{a}}.
a(2) = 2: {{a,aa}, {a,ab}}.
a(3) = 1: {{a,aa,ab}}.
a(4) = 4: {{a,aa,ab,aaa}, {a,aa,ab,aab}, {a,aa,ab,aba}, {a,aa,ab,abc}}.
a(5) = 6: {{a,aa,ab,aaa,aab}, {a,aa,ab,aaa,aba}, {a,aa,ab,aaa,abc}, {a,aa,aab,aba}, {a,aa,ab,aab,ab,abc}, {a,aa,ab,aba,abc}}.
a(6) = 4: {{a,aa,ab,aaa,aab,aba}, {a,aa,ab,aaa,aab,abc}, {a,aa,ab,aaa,aba,abc}, {a,aa,ab,aab,aba,abc}}.
a(7) = 1: {{a,aa,ab,aaa,aab,aba,abc}}.
Breaking the sequence into lines after each 1 gives an irregular triangle whose j-th row equals the A000085(j)-th row of A007318 without its leftmost term. The leftmost column of this triangle is A000085:
   1;
   1;
   2,   1;
   4,   6,    4,     1;
  10,  45,  120,   210,   252,    210,    120,      45,      10,   1;
  26, 325, 2600, 14950, 65780, 230230, 657800, 1562275, 3124550, ...
  ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1115

Crossrefs

Cf. A000085, A007318, A293815, A294129.