cp's OEIS Frontend

A331704 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.

%I A331704 #7 Jan 25 2020 20:54:50
%S A331704 1,1,6,46,544,7983,144970,3097825,76494540,2139610590,66898897827,
%T A331704 2311748912745,87494097274959,3599356204576335,159917091369687135,
%U A331704 7631292367127171222,389282192196378927707,21138914821756778420757,1217459545430430305769230
%N A331704 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 A331704 The condition that the columns be in decreasing order is equivalent to considering nonequivalent matrices with distinct columns up to permutation of columns.
%H A331704 Andrew Howroyd, <a href="/A331704/b331704.txt">Table of n, a(n) for n = 0..200</a>
%F A331704 a(n) = (1/n!)*Sum_{k=0..n} Stirling1(n, k) * A331644(k).
%e A331704 The a(2) = 6 matrices are:
%e A331704    [1 1]  [1 0]  [1 0]  [2 1]  [2 0]  [1 0]
%e A331704    [1 0]  [1 1]  [0 1]  [0 1]  [0 2]  [1 2]
%e A331704    [0 1]  [0 1]  [1 1]
%Y A331704 Row n=2 of A331570.
%Y A331704 Cf. A331644, A331705.
%K A331704 nonn
%O A331704 0,3
%A A331704 _Andrew Howroyd_, Jan 25 2020