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 A247026 Number A(n,k) of endofunctions on [n] that are the k-th power of an endofunction; square array A(n,k), n>=0, k>=0, read by antidiagonals. 17
 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 3, 27, 1, 1, 1, 4, 12, 256, 1, 1, 1, 3, 19, 100, 3125, 1, 1, 1, 4, 12, 116, 1075, 46656, 1, 1, 1, 3, 21, 73, 985, 13356, 823543, 1, 1, 1, 4, 10, 148, 580, 11026, 197764, 16777216, 1, 1, 1, 3, 21, 44, 1281, 5721, 145621, 3403576, 387420489, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS Number of endofunctions f on [n] such that an endofunction g on [n] exists with f=g^k. LINKS EXAMPLE A(3,2) = 12: (1,1,1), (1,1,3), (1,2,1), (1,2,2), (1,2,3), (1,3,3), (2,2,2), (2,2,3), (2,3,1), (3,1,2), (3,2,3), (3,3,3). A(3,6) = 10: (1,1,1), (1,1,3), (1,2,1), (1,2,2), (1,2,3), (1,3,3), (2,2,2), (2,2,3), (3,2,3), (3,3,3). A(4,4) = 73: (1,1,1,1), (1,1,1,4), (1,1,3,1), (1,1,3,3), ..., (4,4,1,3), (4,4,2,3), (4,4,3,4), (4,4,4,4). Square array A(n,k) begins:   1,      1,      1,      1,     1,      1,     1,      1, ...   1,      1,      1,      1,     1,      1,     1,      1, ...   1,      4,      3,      4,     3,      4,     3,      4, ...   1,     27,     12,     19,    12,     21,    10,     21, ...   1,    256,    100,    116,    73,    148,    44,    148, ...   1,   3125,   1075,    985,   580,   1281,   295,   1305, ...   1,  46656,  13356,  11026,  5721,  12942,  3136,  13806, ...   1, 823543, 197764, 145621, 69244, 150955, 42784, 169681, ... MATHEMATICA (* This program is not suitable to compute a large number of terms. *) nmax = 8; f[a_][b_] /; Length[a]==Length[b] := Table[b[[a[[i]]]], {i, 1, Length[a]}]; A[n_, k_] := Nest[f[#], Range[n], k]& /@ Tuples[Range[n], {n}] // Union // Length; Table[A[n-k, k], {n, 0, nmax}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, May 05 2019 *) CROSSREFS Columns k=0-10 give: A000012, A000312, A102687, A163859, A163860, A163861, A247053, A247054, A247055, A247056, A247057. Rows n=0+1, 2-7 give: A000012, A103947, A103948, A103949, A102709, A103950, A247058. Main diagonal gives A247059. Cf. A247005 (the same for permutations). Sequence in context: A010328 A332847 A245501 * A193512 A276330 A234957 Adjacent sequences:  A247023 A247024 A247025 * A247027 A247028 A247029 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Sep 09 2014 STATUS approved

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Last modified April 15 10:49 EDT 2021. Contains 342977 sequences. (Running on oeis4.)