cp's OEIS Frontend

A331316 Number of nonnegative integer matrices with n distinct columns and any number of distinct nonzero rows with each column sum being 2 and rows in decreasing lexicographic order.

%I A331316 #10 Jan 24 2020 15:56:06
%S A331316 1,1,4,27,266,3599,62941,1372117,36248765,1135864306,41501271477,
%T A331316 1743624004536,83268125043937,4476101995389591,268589319338401864,
%U A331316 17860954789864760357,1307982591075162739660,104895999816356419875935,9166919404389461922512723
%N A331316 Number of nonnegative integer matrices with n distinct columns and any number of distinct nonzero rows with each column sum being 2 and rows in decreasing lexicographic order.
%C A331316 The condition that the rows be in decreasing order is equivalent to considering nonequivalent matrices with distinct rows up to permutation of rows.
%H A331316 Andrew Howroyd, <a href="/A331316/b331316.txt">Table of n, a(n) for n = 0..200</a>
%F A331316 a(n) = Sum_{k=0..n} Stirling1(n,k)*A094574(k).
%e A331316 The a(2) = 4 matrices are:
%e A331316    [2 1]   [2 0]   [1 2]   [1 1]
%e A331316    [0 1]   [0 2]   [1 0]   [1 0]
%e A331316                            [0 1]
%Y A331316 Row n=2 of A331160.
%Y A331316 Cf. A094574.
%K A331316 nonn
%O A331316 0,3
%A A331316 _Andrew Howroyd_, Jan 13 2020