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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. 7
 1, 1, 3, 1, 7, 19, 1, 15, 65, 175, 1, 31, 211, 781, 2101, 1, 63, 665, 3367, 11529, 31031, 1, 127, 2059, 14197, 61741, 201811, 543607, 1, 255, 6305, 58975, 325089, 1288991, 4085185, 11012415 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Row sums = A000312. Main diagonal = A045531. LINKS Vincenzo Librandi, Rows n = 1..60, flattened FORMULA T(n,k) = k^n-(k-1)^n. EXAMPLE Triangle begins: 1 1 3 1 7 19 1 15 65 175 1 31 211 781 2101 1 63 665 3367 11529 31031 1 127 2059 14197 61741 201811 543607 etc. MATHEMATICA Table[Table[(1-((i-1)/i)^n) i^n, {i, 1, n}], {n, 1, 8}]//Grid Flatten[Table[k^n - (k-1)^n, {n, 0, 10}, {k, 1, n}]] (* Vincenzo Librandi, Jan 28 2013 *) PROG (Magma) /* As triangle: */ [[k^n - (k-1)^n: k in [1..n]]: n in [1..9]]; // Vincenzo Librandi, Jan 28 2013 CROSSREFS Cf. A022522, A022523. Sequence in context: A282605 A281525 A096643 * A221345 A036575 A347485 Adjacent sequences: A199653 A199654 A199655 * A199657 A199658 A199659 KEYWORD nonn,easy,tabl AUTHOR Geoffrey Critzer, Nov 08 2011 STATUS approved

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Last modified January 29 00:02 EST 2023. Contains 359905 sequences. (Running on oeis4.)