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%I #23 Aug 24 2022 14:42:49
%S 1,3,12,7,56,485,15,240,4015,65280,31,992,32525,1047552,33551307,63,
%T 4032,261415,16773120,1073726199,68719430080,127,16256,2094965,
%U 268419072,34359660243,4398046231168,562949952597769,255,65280,16770655,4294901760,1099511237151
%N Triangle read by rows: T(n,k) is the number of relations from an n-element set to a k-element set that are not functions.
%H Michael De Vlieger, <a href="/A344112/b344112.txt">Table of n, a(n) for n = 1..1275</a> (rows n = 1..50, flattened)
%H Mohammad K. Azarian, <a href="https://doi.org/10.12988/imf.2022.912321">Remarks and Conjectures Regarding Combinatorics of Discrete Partial Functions</a>, Int'l Math. Forum (2022) Vol. 17, No. 3, 129-141.
%F T(n,k) = 2^(n*k) - k^n, n,k >= 1.
%e T(2,2) = (number of relations) - (number of functions) = 2^4 - 4 = 12.
%e Triangle T(n,k) begins:
%e 1;
%e 3, 12;
%e 7, 56, 485;
%e 15, 240, 4015, 65280;
%e 31, 992, 32525, 1047552, 33551307;
%t Column[Table[2^(n*k) - k^n, {n, 10}, {k, n}], Center]
%Y Cf. A101030, A199656, A036679, A344110.
%K easy,nonn,tabl
%O 1,2
%A _Mohammad K. Azarian_, May 10 2021
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