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Number of nonnegative integer matrices with total sum n, nonzero rows and distinct columns each with the same sum with columns in decreasing lexicographic order.
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%I #9 Oct 15 2024 18:06:54

%S 1,3,5,21,17,281,65,3209,10853,47617,1025,3610317,4097,22361569,

%T 570275061,2515267681,65537,229801424781,262145,10805763650257,

%U 114290395025669,39654899669089,4194305,150858428803209493,140094551951590929,98672497472409697

%N Number of nonnegative integer matrices with total sum n, nonzero rows and distinct columns each with the same sum with columns in decreasing lexicographic order.

%C The condition that the columns be in decreasing order is equivalent to considering nonequivalent matrices with distinct columns up to permutation of columns.

%H Andrew Howroyd, <a href="/A331395/b331395.txt">Table of n, a(n) for n = 1..200</a>

%F a(n) = Sum_{d|n} A331278(n/d, d).

%F a(p) = 2^(p-1) + 1 for prime p.

%Y Cf. A331278.

%K nonn

%O 1,2

%A _Andrew Howroyd_, Jan 15 2020