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 A116539 Number of zero-one matrices with n ones and no zero rows or columns and with distinct rows, up to permutation of rows. 26
 1, 1, 2, 7, 28, 134, 729, 4408, 29256, 210710, 1633107, 13528646, 119117240, 1109528752, 10889570768, 112226155225, 1210829041710, 13640416024410, 160069458445202, 1952602490538038, 24712910192430620, 323964329622503527, 4391974577299578248, 61488854148194151940 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the number of labeled hypergraphs spanning an initial interval of positive integers with edge-sizes summing to n. - Gus Wiseman, Dec 18 2018 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..300 P. J. Cameron, T. Prellberg and D. Stark, Asymptotics for incidence matrix classes , arXiv:math/0510155 [math.CO], 2005-2006. M. Klazar, Extremal problems for ordered hypergraphs, arXiv:math/0305048 [math.CO], 2003. EXAMPLE From Gus Wiseman, Dec 18 2018: (Start) The a(3) = 7 edge-sets:     {{1,2,3}}    {{1},{1,2}}    {{2},{1,2}}    {{1},{2,3}}    {{2},{1,3}}    {{3},{1,2}}   {{1},{2},{3}} Inequivalent representatives of the a(4) = 28 0-1 matrices:   [1111] .   [100][1000][010][0100][001][0010][0001][110][110][1100][101][1010][1001]   [111][0111][111][1011][111][1101][1110][101][011][0011][011][0101][0110] .   [10][100][100][1000][100][100][1000][1000][010][010][0100][0100][0010]   [01][010][010][0100][001][001][0010][0001][001][001][0010][0001][0001]   [11][101][011][0011][110][011][0101][0110][110][101][1001][1010][1100] .   [1000]   [0100]   [0010]   [0001] (End) MAPLE b:= proc(n, i, k) b(n, i, k):=`if`(n=0, 1, `if`(i<1, 0, add(b(n-i*j,       min(n-i*j, i-1), k)*binomial(binomial(k, i), j), j=0..n/i)))     end: a:= n-> add(add(b(n\$2, i)*(-1)^(k-i)*binomial(k, i), i=0..k), k=0..n): seq(a(n), n=0..23);  # Alois P. Heinz, Sep 13 2019 MATHEMATICA b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i*j, Min[n - i*j, i - 1], k]*Binomial[Binomial[k, i], j], {j, 0, n/i}]]]; a[n_] := Sum[Sum[b[n, n, i]*(-1)^(k-i)*Binomial[k, i], {i, 0, k}], {k, 0, n}]; a /@ Range[0, 23] (* Jean-François Alcover, Feb 25 2020, after Alois P. Heinz *) CROSSREFS Binary matrices with distinct rows and columns, various versions: A059202, A088309, A088310, A088616, A089673, A089674, A093466, A094000, A094223, A116532, A116539, A181230, A259763 Cf. A049311, A058891, A101370, A255906, A283877, A306021, A319190. Row sums of A326914 and of A326962. Sequence in context: A052319 A127783 A297195 * A266467 A141318 A276080 Adjacent sequences:  A116536 A116537 A116538 * A116540 A116541 A116542 KEYWORD nonn AUTHOR Vladeta Jovovic, Mar 27 2006 EXTENSIONS a(0)=1 prepended and more terms added by Alois P. Heinz, Sep 13 2019 STATUS approved

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Last modified November 23 13:02 EST 2020. Contains 338590 sequences. (Running on oeis4.)