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%I #8 Jan 31 2020 14:46:55
%S 1,3,13,87,539,2483,14567,81669,402187,2089413,10344053,49065413,
%T 232941293,1092284091,5011510213,22637050383,100092546203,
%U 439274499155,1888145728847,8058486875493,33954688300771,140741748208701,579404121062837,2354567807958773,9481400353625789
%N Number of nonnegative integer matrices with 2 columns and any number of distinct nonzero rows with column sums n.
%H Andrew Howroyd, <a href="/A331646/b331646.txt">Table of n, a(n) for n = 0..100</a>
%e The a(1) = 3 matrices are:
%e [1 0] [0 1] [1 1]
%e [0 1] [1 0]
%o (PARI) a(n)={subst(serlaplace(polcoef(polcoef(prod(i=0, n, prod(j=0, n, 1 + x^i*y^j*z + O(x*x^n) + O(y*y^n))), n, x), n, y)/(1 + z)), z, 1)}
%Y Column k=2 of A331568.
%Y Cf. A331647, A331706, A331711.
%K nonn
%O 0,2
%A _Andrew Howroyd_, Jan 23 2020
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