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 A319519 Number of sets of nonempty words with a total of 2n letters over n-ary alphabet such that all n letters occur at least once in the set. 3
 1, 1, 38, 2811, 375698, 78808600, 23761098837, 9706198156760, 5148887208055692, 3435636331820210328, 2812707955072045999940, 2769473851247907714803299, 3226373218837374171864997818, 4386692184929838579321027664266, 6880627149087717821279760600127300 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..214 FORMULA a(n) = A319501(2n,n). EXAMPLE a(0) = 1: {}. a(1) = 1: {aa}. a(2) = 38: {aaab}, {aaba}, {aabb}, {abaa}, {abab}, {abba}, {abbb}, {baaa}, {baab}, {baba}, {babb}, {bbaa}, {bbab}, {bbba}, {a,aab}, {a,aba}, {a,abb}, {a,baa}, {a,bab}, {a,bba}, {a,bbb}, {aa,ab}, {aa,ba}, {aa,bb}, {aaa,b}, {aab,b}, {ab,ba}, {ab,bb}, {aba,b}, {abb,b}, {b,baa}, {b,bab}, {b,bba}, {ba,bb}, {a,aa,b}, {a,ab,b}, {a,b,ba}, {a,b,bb}. 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((-1)^i*binomial(n, i)*h(2*n\$2, n-i), i=0..n): seq(a(n), n=0..15); MATHEMATICA h[n_, i_, k_] := h[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[h[n-i*j, i-1, k]*Binomial[k^i, j], {j, 0, n/i}]]]; a[n_] := Sum[(-1)^i*Binomial[n, i]*h[2n, 2n, n-i], {i, 0, n}]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, May 10 2022, after Alois P. Heinz *) CROSSREFS Cf. A257742, A319501. Sequence in context: A272036 A055605 A217342 * A221111 A322331 A282962 Adjacent sequences: A319516 A319517 A319518 * A319520 A319521 A319522 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 21 2018 STATUS approved

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Last modified December 6 10:00 EST 2023. Contains 367600 sequences. (Running on oeis4.)