%I #6 Jan 31 2020 20:14:24
%S 1,11,66,278,966,2957,8149,20676,48911,108942,230201,464528,899633,
%T 1679685,3034620
%N Number of non-isomorphic set-systems with 4 sets each with n elements.
%C a(n) is the number of nonequivalent binary matrices with 4 distinct columns and any number of nonzero rows with n ones in every column up to permutation of rows and columns.
%e The a(2) = 11 matrices are:
%e [1 0 0 0] [1 1 0 0] [1 1 1 0] [1 1 0 0] [1 1 0 0]
%e [1 0 0 0] [1 0 0 0] [1 0 0 0] [1 0 1 0] [1 0 0 0]
%e [0 1 0 0] [0 1 0 0] [0 1 0 0] [0 1 0 0] [0 1 0 0]
%e [0 1 0 0] [0 0 1 0] [0 0 1 0] [0 0 1 0] [0 0 1 1]
%e [0 0 1 0] [0 0 1 0] [0 0 0 1] [0 0 0 1] [0 0 1 0]
%e [0 0 1 0] [0 0 0 1] [0 0 0 1] [0 0 0 1] [0 0 0 1]
%e [0 0 0 1] [0 0 0 1]
%e [0 0 0 1]
%e .
%e [1 1 1 1] [1 1 1 0] [1 1 0 0] [1 1 0 0] [1 1 0 1] [1 1 0 0]
%e [1 0 0 0] [1 0 0 1] [1 0 1 0] [1 0 1 0] [1 0 1 0] [1 0 1 0]
%e [0 1 0 0] [0 1 0 0] [0 1 1 0] [0 1 0 1] [0 1 1 0] [0 1 0 1]
%e [0 0 1 0] [0 0 1 0] [0 0 0 1] [0 0 1 0] [0 0 0 1] [0 0 1 1]
%e [0 0 0 1] [0 0 0 1] [0 0 0 1] [0 0 0 1]
%e .
%e A set system corresponding to the first of these is {{1,2}, {3,4}, {5,6}, {7,8}}.
%Y Column k=4 of A331508.
%Y Cf. A331714.
%K nonn,more
%O 1,2
%A _Andrew Howroyd_, Jan 31 2020