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%I #6 Jan 25 2020 02:27:49
%S 1,1,1,4,1,18,1,231,185,3265,1,78115,1,1287063,2711905,32669406,1,
%T 1568741156,1,29488026590,232383728379,967596779632,1,147586156446663,
%U 585810653617,1509052435744561,61466235823794522,96920622619890141,1,47758782949643628393
%N Number of binary matrices with distinct nonzero rows, a total of n ones and distinct columns each with the same number of ones and columns in decreasing lexicographic order.
%C The condition that the columns be in decreasing order is equivalent to considering nonequivalent matrices with distinct columns up to permutation of columns.
%F a(n) = Sum_{d|n} A331569(n/d, d).
%e The a(4) = 4 matrices are:
%e [1 0 0 0] [1 1] [1 0] [1 0]
%e [0 1 0 0] [1 0] [1 1] [0 1]
%e [0 0 1 0] [0 1] [0 1] [1 1]
%e [0 0 0 1]
%Y Cf. A331569.
%K nonn
%O 1,4
%A _Andrew Howroyd_, Jan 24 2020
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