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A199656 Triangular array read by rows, T(n,k) is the number of functions from {1,2,...,n} into {1,2,...,n} with maximum value of k.

%I A199656 #22 Jul 28 2025 14:54:26
%S A199656 1,1,3,1,7,19,1,15,65,175,1,31,211,781,2101,1,63,665,3367,11529,31031,
%T A199656 1,127,2059,14197,61741,201811,543607,1,255,6305,58975,325089,1288991,
%U A199656 4085185,11012415,1,511,19171,242461,1690981,8124571,30275911,93864121,253202761
%N A199656 Triangular array read by rows, T(n,k) is the number of functions from {1,2,...,n} into {1,2,...,n} with maximum value of k.
%C A199656 Row sums = A000312.
%C A199656 Main diagonal = A045531.
%H A199656 Vincenzo Librandi, <a href="/A199656/b199656.txt">Rows n = 1..60, flattened</a>
%F A199656 T(n,k) = k^n-(k-1)^n.
%e A199656 Triangle begins:
%e A199656   1
%e A199656   1    3
%e A199656   1    7   19
%e A199656   1   15   65   175
%e A199656   1   31  211   781   2101
%e A199656   1   63  665  3367  11529   31031
%e A199656   1  127 2059 14197  61741  201811  543607
%e A199656   ...
%t A199656 Table[Table[(1-((i-1)/i)^n) i^n,{i,1,n}],{n,1,8}]//Grid
%t A199656 Flatten[Table[k^n - (k-1)^n, {n, 0, 10}, {k, 1, n}]] (* _Vincenzo Librandi_, Jan 28 2013 *)
%o A199656 (Magma) /* As triangle: */ [[k^n - (k-1)^n: k in [1..n]]: n in [1..9]]; // _Vincenzo Librandi_, Jan 28 2013
%Y A199656 Cf. A022522, A022523.
%K A199656 nonn,easy,tabl
%O A199656 1,3
%A A199656 _Geoffrey Critzer_, Nov 08 2011