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 A318395 Number of nonnegative integer matrices with values summing to n, up to transposition and permutation of rows and columns. 1
 1, 1, 3, 7, 21, 54, 167, 491, 1586, 5132, 17442, 60399, 216172, 790436, 2965333, 11365813, 44536775, 178107679, 726716229, 3022464373, 12807206008, 55253891494, 242585471236, 1083255591604, 4917631017573, 22685090928596, 106291554085987, 505653658171936, 2441383079595849 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the number of non-isomorphic pairs of set partitions of {1,...,n}. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..50 FORMULA a(n) = (A007716(n) + A316983(n))/2. - Andrew Howroyd, Sep 03 2018 EXAMPLE Inequivalent representatives of the a(3) = 7 nonnegative integer matrices:   [3]   [1 2]   [1 1 1]   [1 0]   [0 1]   [1 0 0]   [1 0 0]                           [0 2]   [1 1]   [0 1 1]   [0 1 0]                                                     [0 0 1] Non-isomorphic representatives of the a(3) = 7 pairs of set partitions:     {{1,2,3}}     {{1,2,3}}     {{1,2,3}}    {{1},{2,3}}     {{1,2,3}}   {{1},{2},{3}}    {{1},{2,3}}   {{1},{2,3}}    {{1},{2,3}}   {{2},{1,3}}    {{1},{2,3}}  {{1},{2},{3}}   {{1},{2},{3}} {{1},{2},{3}} CROSSREFS Cf. A000110, A000258, A001247, A007716, A008277, A049311, A059849, A060639, A116540, A181939, A316983, A318393. Sequence in context: A098545 A161707 A192068 * A151267 A319558 A307251 Adjacent sequences:  A318392 A318393 A318394 * A318396 A318397 A318398 KEYWORD nonn AUTHOR Gus Wiseman, Aug 25 2018 EXTENSIONS a(6)-a(25) from Andrew Howroyd, Sep 03 2018 Terms a(26) and beyond from Andrew Howroyd, Mar 29 2020 STATUS approved

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Last modified May 26 02:56 EDT 2020. Contains 334613 sequences. (Running on oeis4.)