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A331389 Number of binary matrices with n distinct columns and any number of nonzero rows with 3 ones in every column and rows in nonincreasing lexicographic order.

%I A331389 #11 Jan 31 2020 14:32:09
%S A331389 1,1,3,29,666,28344,1935054,193926796,26892165502,4946464286746,
%T A331389 1168900475263013,346080409272270888,125798338606148948325,
%U A331389 55204084562033205121607,28834556615453989801860765,17710828268156331289770544579,12658784968736373972502731143309
%N A331389 Number of binary matrices with n distinct columns and any number of nonzero rows with 3 ones in every column and rows in nonincreasing lexicographic order.
%C A331389 The condition that the rows be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of rows.
%C A331389 a(n) is the number of T_0 3-regular set multipartitions (multisets of sets) on an n-set.
%H A331389 Andrew Howroyd, <a href="/A331389/b331389.txt">Table of n, a(n) for n = 0..100</a>
%F A331389 a(n) = Sum_{k=0..n} Stirling1(n,k)*A165434(k). - _Andrew Howroyd_, Jan 31 2020
%e A331389 The a(2) = 3 matrices are:
%e A331389    [1 0]   [1 1]   [1 1]
%e A331389    [1 0]   [1 0]   [1 1]
%e A331389    [1 0]   [1 0]   [1 0]
%e A331389    [0 1]   [0 1]   [0 1]
%e A331389    [0 1]   [0 1]
%e A331389    [0 1]
%Y A331389 Row n=3 of A331126.
%Y A331389 Cf. A165434.
%K A331389 nonn
%O A331389 0,3
%A A331389 _Andrew Howroyd_, Jan 15 2020