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 A211318 Triangle read by rows: number of permutations of 1..n by length l of longest run (n >= 1, 1 <= l <= n). 16
 1, 0, 2, 0, 4, 2, 0, 10, 12, 2, 0, 32, 70, 16, 2, 0, 122, 442, 134, 20, 2, 0, 544, 3108, 1164, 198, 24, 2, 0, 2770, 24216, 10982, 2048, 274, 28, 2, 0, 15872, 208586, 112354, 22468, 3204, 362, 32, 2, 0, 101042, 1972904, 1245676, 264538, 39420, 4720, 462, 36, 2, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 262. (Contains errors for n >= 13.) Sean A. Irvine, Posting to Sequence Fans Mailing List, May 02 2012 LINKS Wouter Meeussen and Alois P. Heinz, Rows n = 1..70, flattened (rows n = 1..16 from Wouter Meeussen) Max A. Alekseyev, On the number of permutations with bounded run lengths, arXiv:1205.4581 [math.CO], 2012-2013. [From N. J. A. Sloane, Oct 23 2012] EXAMPLE Triangle begins: n l=1, l=2, l=3, etc... 1 [1] 2 [0, 2] 3 [0, 4, 2] 4 [0, 10, 12, 2] 5 [0, 32, 70, 16, 2] 6 [0, 122, 442, 134, 20, 2] 7 [0, 544, 3108, 1164, 198, 24, 2] 8 [0, 2770, 24216, 10982, 2048, 274, 28, 2] 9 [0, 15872, 208586, 112354, 22468, 3204, 362, 32, 2] 10 [0, 101042, 1972904, 1245676, 264538, 39420, 4720, 462, 36, 2] 11 [0, 707584, 20373338, 14909340, 3340962, 514296, 64020, 6644, 574, 40, 2] 12 [0, 5405530, 228346522, 191916532, 45173518, 7137818, 913440, 98472, 9024, 698, 44, 2] 13 [0, 44736512, 2763212980, 2646100822, 652209564, 105318770, 13760472, 1523808, 145080, 11908, 834, 48, 2] 14 [0, 398721962, 35926266244, 38932850396, 10024669626, 1649355338, 219040274, 24744720, 2419872, 206388, 15344, 982, 52, 2] 15 [0, 3807514624, 499676669254, 609137502242, 163546399460, 27356466626, 3681354658, 422335056, 42129360, 3690960, 285180, 19380, 1142, 56, 2], ... More rows than usual are shown, in order to correct errors in David, Kendall and Barton. MATHEMATICA <1, 1] = 0; Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Aug 18 2018, after Alois P. Heinz *) CROSSREFS Mirror image of triangle in A010026. Columns l=2-10 give: A001250, A001251, A001252, A001253, A230129, A230130, A230131, A230132, A230133. Sequence in context: A144289 A293815 A339941 * A324239 A274706 A037035 Adjacent sequences:  A211315 A211316 A211317 * A211319 A211320 A211321 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, May 02 2012, based on computations by Sean A. Irvine. STATUS approved

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Last modified July 24 23:25 EDT 2021. Contains 346273 sequences. (Running on oeis4.)