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%I #5 Jan 25 2020 02:22:41
%S 1,1,1,2,1,6,1,44,6,519,1,8363,1,163357,9427,3988615,1,117148318,1,
%T 3986012464,84012192,157783127674,1,7143740399835,248686,
%U 364166073164915,2479642897110,20827974319925302,1,1324585467847848929,1,92917902002561639120,190678639438170503
%N Number of binary matrices with a total of n ones, distinct columns each with the same number of ones and distinct nonzero rows in decreasing lexicographic order.
%C The condition that the rows be in decreasing order is equivalent to considering nonequivalent matrices with distinct rows up to permutation of rows.
%F a(n) = Sum_{d|n} A331039(n/d, d).
%e The a(6) = 6 matrices are:
%e [1 0 0 0 0 0] [1 1 1] [1 1 0] [1 1 0] [1 0 1] [1 1 0]
%e [0 1 0 0 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] [1 0 1]
%e [0 0 1 0 0 0] [0 1 0] [0 1 0] [0 1 1] [0 1 1] [0 1 1]
%e [0 0 0 1 0 0] [0 0 1] [0 0 1] [0 0 1] [0 1 0]
%e [0 0 0 0 1 0]
%e [0 0 0 0 0 1]
%Y Cf. A331039.
%K nonn
%O 1,4
%A _Andrew Howroyd_, Jan 24 2020
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