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Number of n X n matrices whose values cover an initial interval of positive integers and whose rows and columns have values which are strictly increasing.
4

%I #11 Sep 16 2024 23:59:41

%S 1,1,3,197,732963,289599115433,19454710000290140631,

%T 324252739440855086589750626125,

%U 1839663535877691613435674541258128354870051,4664717625821787781559533555514908690826684467996898799881,6714190347498763079980307954946450922919624466513063316268554904936722083543

%N Number of n X n matrices whose values cover an initial interval of positive integers and whose rows and columns have values which are strictly increasing.

%H Andrew Howroyd, <a href="/A374514/a374514.gp.txt">PARI Program</a>, Sep 2024.

%e The a(2) = 3 matrices are:

%e [1 2] [1 2] [1 3]

%e [2 3] [3 4] [2 4]

%o (PARI) \\ See Links section for program file.

%o vector(8, n, A374514(n-1))

%Y Main diagonal of A374985.

%Y Cf. A039622 (case all values also distinct), A068942, A376162 (case for symmetric matrices).

%K nonn

%O 0,3

%A _Andrew Howroyd_, Sep 16 2024