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.

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

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