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 A000303 Number of permutations of [n] in which the longest increasing run has length 2. (Formerly M3522 N1430) 7
 0, 1, 4, 16, 69, 348, 2016, 13357, 99376, 822040, 7477161, 74207208, 797771520, 9236662345, 114579019468, 1516103040832, 21314681315997, 317288088082404, 4985505271920096, 82459612672301845, 1432064398910663704, 26054771465540507272 (list; 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. 261, Table 7.4.1. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..464 (first 100 terms from Max Alekseyev) Max A. Alekseyev, On the number of permutations with bounded runs length, arXiv preprint arXiv:1205.4581 [math.CO], 2012-2013. - From N. J. A. Sloane, Oct 23 2012 EXAMPLE a(3)=4 because we have (13)2, 2(13), (23)1, 3(12), where the parentheses surround increasing runs of length 2. MATHEMATICA b[u_, o_, t_, k_] := b[u, o, t, k] = If[t == k, (u + o)!, If[Max[t, u] + o < k, 0, Sum[b[u + j - 1, o - j, t + 1, k], {j, 1, o}] + Sum[b[u - j, o + j - 1, 1, k], {j, 1, u}]]]; T[n_, k_] := b[0, n, 0, k] - b[0, n, 0, k + 1]; a[n_] := T[n, 2]; Array[a, 30] (* Jean-François Alcover, Jul 19 2018, after Alois P. Heinz *) CROSSREFS Column 2 of A008304. Other columns: A000402, A000434, A000456, A000467, A230055. Cf. A001250, A001251, A001252, A001253, A010026, A211318. Equals 1 less than A049774. - Greg Dresden, Feb 22 2020 Sequence in context: A339045 A341255 A231358 * A298048 A144316 A180145 Adjacent sequences:  A000300 A000301 A000302 * A000304 A000305 A000306 KEYWORD nonn AUTHOR EXTENSIONS Better description from Emeric Deutsch, May 08 2004 Edited and extended by Max Alekseyev, May 20 2012 STATUS approved

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Last modified April 11 18:59 EDT 2021. Contains 342888 sequences. (Running on oeis4.)