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 A231777 Number T(n,k) of permutations of [n] with exactly k ascents from odd to even numbers; triangle T(n,k), n>=0, 0<=k<=floor(n/2), read by rows. 2
 1, 1, 1, 1, 4, 2, 8, 14, 2, 54, 60, 6, 162, 402, 150, 6, 1536, 2712, 768, 24, 6144, 19704, 12744, 1704, 24, 75000, 183120, 94320, 10320, 120, 375000, 1473720, 1392720, 365520, 21720, 120, 5598720, 17522640, 13631040, 3011040, 152640, 720, 33592320, 156250800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Rows n = 0..23, flattened EXAMPLE T(4,0) = 8: 1324, 2413, 2431, 3241, 4132, 4213, 4231, 4321. T(4,1) = 14: 1243, 1342, 1423, 1432, 2134, 2143, 2314, 2341, 3124, 3142, 3214, 3421, 4123, 4312. T(4,2) = 2: 1234, 3412. T(5,2) = 6: 12345, 12534, 34125, 34512, 51234, 53412. T(6,3) = 6: 123456, 125634, 341256, 345612, 561234, 563412. Triangle T(n,k) begins: : 0 : 1; : 1 : 1; : 2 : 1, 1; : 3 : 4, 2; : 4 : 8, 14, 2; : 5 : 54, 60, 6; : 6 : 162, 402, 150, 6; : 7 : 1536, 2712, 768, 24; : 8 : 6144, 19704, 12744, 1704, 24; : 9 : 75000, 183120, 94320, 10320, 120; : 10 : 375000, 1473720, 1392720, 365520, 21720, 120; CROSSREFS Column k=0 gives: A231601. Row sums and T(2n,n) give: A000142. T(n,floor(n/2)) gives: A081123(n+1). Cf. A004526. Sequence in context: A064821 A002291 A225872 * A288181 A110622 A130078 Adjacent sequences: A231774 A231775 A231776 * A231778 A231779 A231780 KEYWORD nonn,tabf AUTHOR Alois P. Heinz, Nov 13 2013 STATUS approved

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Last modified August 15 04:38 EDT 2024. Contains 375172 sequences. (Running on oeis4.)