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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: A051239 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 February 20 22:47 EST 2020. Contains 332086 sequences. (Running on oeis4.)