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 A068313 Number of (0,1)-matrices with sum of entries equal to n and no zero rows or columns, with weakly decreasing row sums and column sums. 12
 1, 4, 15, 82, 457, 3231, 24055, 209375, 1955288, 20455936, 229830841, 2828166755, 37228913365, 528635368980, 7990596990430, 128909374528433, 2202090635802581, 39837079499488151, 759320365206705013 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is the sum over the matrix of base change from the elementary symmetric functions to the monomial symmetric functions REFERENCES I. G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford 1979, p. 57 LINKS EXAMPLE a(2) = 4 because there 4 different 0-1 matrices of weight 2, these are 1 10 01 11,1, 01, 10 From Gus Wiseman, Nov 15 2018: (Start) The a(3) = 15 matrices:   [1 1 1] .   [1 1] [1 1 0] [1 0 1] [0 1 1]   [1 0] [0 0 1] [0 1 0] [1 0 0] .   [1] [1 0] [1 0] [1 0 0] [1 0 0] [0 1] [0 1 0] [0 1 0] [0 0 1] [0 0 1]   [1] [1 0] [0 1] [0 1 0] [0 0 1] [1 0] [1 0 0] [0 0 1] [1 0 0] [0 1 0]   [1] [0 1] [1 0] [0 0 1] [0 1 0] [1 0] [0 0 1] [1 0 0] [0 1 0] [1 0 0] (End) MATHEMATICA prs2mat[prs_]:=Table[Count[prs, {i, j}], {i, Union[First/@prs]}, {j, Union[Last/@prs]}]; Table[Length[Select[Subsets[Tuples[Range[n], 2], {n}], And[Union[First/@#]==Range[Max@@First/@#], Union[Last/@#]==Range[Max@@Last/@#], OrderedQ[Total/@prs2mat[#]], OrderedQ[Total/@T[prs2mat[#]]]]&]], {n, 5}] (* Gus Wiseman, Nov 15 2018 *) CROSSREFS Cf. A000219, A001970, A007716, A049311, A101370, A117433, A120733, A321646, A321652, A321653, A321654. Sequence in context: A125307 A073479 A147690 * A174661 A207161 A203121 Adjacent sequences:  A068310 A068311 A068312 * A068314 A068315 A068316 KEYWORD nonn AUTHOR Axel Kohnert (axel.kohnert(AT)uni-bayreuth.de), Feb 25 2002 EXTENSIONS Name changed by Gus Wiseman, Nov 15 2018 STATUS approved

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Last modified October 1 17:45 EDT 2020. Contains 337444 sequences. (Running on oeis4.)