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 A319518 Number of sets of nonempty words with a total of n letters over n-ary alphabet such that if a letter occurs in the set all predecessors occur at least once. 4
 1, 1, 4, 27, 218, 2178, 25529, 343392, 5205948, 87740878, 1626182463, 32852520594, 718169744206, 16883948532684, 424649281630018, 11374387591643065, 323183885622356184, 9706973096869527210, 307248234238900686688, 10220414166250239718518 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..300 EXAMPLE a(0) = 1: {}. a(1) = 1: {a}. a(2) = 4: {aa}, {ab}, {ba}, {a,b}. a(3) = 27: {aaa}, {aab}, {aba}, {abb}, {abc}, {acb}, {baa}, {bab}, {bac}, {bba}, {bca}, {cab}, {cba}, {a,aa}, {a,ab}, {a,ba}, {a,bb}, {a,bc}, {a,cb}, {aa,b}, {ab,b}, {ab,c}, {ac,b}, {b,ba}, {b,ca}, {ba,c}, {a,b,c}. MAPLE h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,       add(h(n-i*j, i-1, k)*binomial(k^i, j), j=0..n/i)))     end: a:= n-> add(add((-1)^i*binomial(k, i)*h(n\$2, k-i), i=0..k), k=0..n): seq(a(n), n=0..20); CROSSREFS Row sums of A319501. Cf. A257741. Sequence in context: A059391 A190738 A275607 * A304045 A317103 A341962 Adjacent sequences:  A319515 A319516 A319517 * A319519 A319520 A319521 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 21 2018 STATUS approved

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Last modified January 26 13:42 EST 2022. Contains 350598 sequences. (Running on oeis4.)