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 A276837 Number A(n,k) of permutations of [n] such that for each cycle c the smallest integer interval containing all elements of c has at most k elements; square array A(n,k), n>=0, k>=0, read by antidiagonals. 11
 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 2, 3, 1, 0, 1, 1, 2, 6, 5, 1, 0, 1, 1, 2, 6, 12, 8, 1, 0, 1, 1, 2, 6, 24, 25, 13, 1, 0, 1, 1, 2, 6, 24, 60, 57, 21, 1, 0, 1, 1, 2, 6, 24, 120, 150, 124, 34, 1, 0, 1, 1, 2, 6, 24, 120, 360, 399, 268, 55, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS The sequence of column k satisfies a linear recurrence with constant coefficients of order 2^(k-1) for k>0. LINKS Alois P. Heinz, Antidiagonals n = 0..30, flattened Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019 FORMULA A(n,k+1) - A(n,k) = A263757(n,k) for n>0. EXAMPLE Square array A(n,k) begins:   1, 1,  1,   1,    1,    1,    1,     1,     1, ...   0, 1,  1,   1,    1,    1,    1,     1,     1, ...   0, 1,  2,   2,    2,    2,    2,     2,     2, ...   0, 1,  3,   6,    6,    6,    6,     6,     6, ...   0, 1,  5,  12,   24,   24,   24,    24,    24, ...   0, 1,  8,  25,   60,  120,  120,   120,   120, ...   0, 1, 13,  57,  150,  360,  720,   720,   720, ...   0, 1, 21, 124,  399, 1050, 2520,  5040,  5040, ...   0, 1, 34, 268, 1145, 3192, 8400, 20160, 40320, ... CROSSREFS Columns k=0-10 give: A000007, A000012, A000045(n+1), A214663, A276838, A276839, A276840, A276841, A276842, A276843, A276844. Main diagonal gives A000142. Cf. A263757, A276719. Sequence in context: A182172 A143841 A276719 * A269941 A035440 A029878 Adjacent sequences:  A276834 A276835 A276836 * A276838 A276839 A276840 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Sep 20 2016 STATUS approved

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Last modified June 21 04:10 EDT 2021. Contains 345354 sequences. (Running on oeis4.)