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%I #8 Jan 15 2020 18:41:57
%S 1,2,2,4,2,14,2,76,31,801,2,12797,2,233247,28480,5560377,2,160866915,
%T 2,5351339038,193927186,208746406130,2,9342273087807,5289613,
%U 470405726166256,4946464287635,26636935297440055,2,1679266767908385729,2,116818412262277969513
%N Number of binary matrices with a total of n ones, distinct columns each with the same number of ones and nonzero rows in nonincreasing lexicographic order.
%C The condition that the rows be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of rows.
%F a(n) = Sum{d|n} A331126(n/d, d).
%F a(p) = 2 for prime p.
%e The a(4) = 4 matrices are:
%e [1 0 0 0] [1] [1 0] [1 1]
%e [0 1 0 0] [1] [1 0] [1 0]
%e [0 0 1 0] [1] [0 1] [0 1]
%e [0 0 0 1] [1] [0 1]
%Y Cf. A331126.
%K nonn
%O 1,2
%A _Andrew Howroyd_, Jan 15 2020
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