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 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. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) is the smallest nonzero term in column k of A293815. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1115 EXAMPLE 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, ... CROSSREFS Cf. A000085, A007318, A293815, A294129. Sequence in context: A043302 A343964 A345135 * A143897 A217298 A217299 Adjacent sequences:  A291054 A291055 A291056 * A291058 A291059 A291060 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 20 2017 STATUS approved

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Last modified December 8 22:49 EST 2021. Contains 349596 sequences. (Running on oeis4.)