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Number of nonnegative integer matrices with n distinct columns and any number of distinct nonzero rows with column sums 2 and columns in decreasing lexicographic order.
3

%I #7 Jan 25 2020 20:54:50

%S 1,1,6,46,544,7983,144970,3097825,76494540,2139610590,66898897827,

%T 2311748912745,87494097274959,3599356204576335,159917091369687135,

%U 7631292367127171222,389282192196378927707,21138914821756778420757,1217459545430430305769230

%N Number of nonnegative integer matrices with n distinct columns and any number of distinct nonzero rows with column sums 2 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.

%H Andrew Howroyd, <a href="/A331704/b331704.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = (1/n!)*Sum_{k=0..n} Stirling1(n, k) * A331644(k).

%e The a(2) = 6 matrices are:

%e [1 1] [1 0] [1 0] [2 1] [2 0] [1 0]

%e [1 0] [1 1] [0 1] [0 1] [0 2] [1 2]

%e [0 1] [0 1] [1 1]

%Y Row n=2 of A331570.

%Y Cf. A331644, A331705.

%K nonn

%O 0,3

%A _Andrew Howroyd_, Jan 25 2020