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 A116540 Number of zero-one matrices with n ones and no zero rows or columns, up to permutation of rows. 13
 1, 3, 10, 41, 192, 1025, 6087, 39754, 282241, 2159916, 17691161, 154192692, 1423127819, 13851559475, 141670442163, 1517880400352, 16989834719706, 198191448685735, 2404300796114642, 30273340418567819, 394948562421362392 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also number of normal set multipartitions of weight n. These are defined as multisets of sets that together partition a normal multiset of weight n, where a multiset is normal if it spans an initial interval of positive integers. Set multipartitions are involved in the expansion of elementary symmetric functions in terms of augmented monomial symmetric functions. - Gus Wiseman, Oct 22 2015 LINKS 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. Gus Wiseman, Four symmetric function identities EXAMPLE The a(3) = 10 normal set multipartitions are: {1,1,1}, {1,12}, {1,1,2}, {2,12}, {1,2,2}, {123}, {1,23}, {2,13}, {3,12}, {1,2,3}. MATHEMATICA MSOSA[s_List] :=   MSOSA[s] = If[Length[s] === 0, {{}}, Module[{sbs, fms},      sbs = Rest[Subsets[Union[s]]];      fms =       Function[r,         Append[#, r] & /@          MSOSA[Fold[DeleteCases[#1, #2, {1}, 1] &, s, r]]] /@ sbs;      Select[Join @@ fms, OrderedQ]      ]]; mmallnorm[n_Integer] :=   Function[s, Array[Count[s, y_ /; y <= #] + 1 &, n]] /@    Subsets[Range[n - 1] + 1]; Array[Plus @@ Length /@ MSOSA /@ mmallnorm[#] &, 9] (* Gus Wiseman, Oct 22 2015 *) CROSSREFS Cf. A049311, A101370. Sequence in context: A151083 A140046 A260772 * A236407 A000248 A245504 Adjacent sequences:  A116537 A116538 A116539 * A116541 A116542 A116543 KEYWORD nonn AUTHOR Vladeta Jovovic, Mar 27 2006 STATUS approved

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Last modified August 18 20:29 EDT 2018. Contains 313840 sequences. (Running on oeis4.)