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A303648 Number T(n,k) of involutions of [n] having exactly k peaks; triangle T(n,k), n>=0, 0<=k<=max(0,floor((n-1)/2)), read by rows. 2
1, 1, 2, 3, 1, 4, 6, 5, 18, 3, 6, 44, 26, 7, 91, 123, 11, 8, 172, 448, 136, 9, 300, 1348, 912, 51, 10, 496, 3600, 4552, 838, 11, 781, 8704, 18476, 7441, 283, 12, 1186, 19584, 65324, 48116, 5930, 13, 1742, 41379, 206556, 250375, 66606, 1833, 14, 2492, 83210, 600456, 1120042, 536908, 47358 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..56.

Wikipedia, Involution

FORMULA

T(2n+1,n) = A072187(n+1).

EXAMPLE

T(5,0) = 5: 12345, 21345, 32145, 43215, 54321.

T(5,1) = 18: 12354, 12435, 12543, 13245, 14325, 14523, 15432, 21354, 21435, 21543, 32154, 34125, 42315, 42513, 45312, 52341, 52431, 53241.

T(5,2) = 3: 13254, 15342, 35142.

Triangle T(n,k) begins:

   1;

   1;

   2;

   3,    1;

   4,    6;

   5,   18,     3;

   6,   44,    26;

   7,   91,   123,     11;

   8,  172,   448,    136;

   9,  300,  1348,    912,     51;

  10,  496,  3600,   4552,    838;

  11,  781,  8704,  18476,   7441,   283;

  12, 1186, 19584,  65324,  48116,  5930;

  13, 1742, 41379, 206556, 250375, 66606, 1833;

CROSSREFS

Row sums give A000085.

Columns k=0-1 give: A028310, A303649.

Cf. A008303 (the same for permutations), A072187, A303564 (the same for derangements).

Sequence in context: A235715 A129566 A073809 * A298364 A111776 A189187

Adjacent sequences:  A303645 A303646 A303647 * A303649 A303650 A303651

KEYWORD

nonn,tabf

AUTHOR

Alois P. Heinz, Apr 27 2018

STATUS

approved

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Last modified May 8 20:32 EDT 2021. Contains 343668 sequences. (Running on oeis4.)