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

Author

Alois P. Heinz, Nov 13 2013

Keywords

• nonn
• tabf

Examples

			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;
		

Links

• Alois P. Heinz, Rows n = 0..23, flattened

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.