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A152662 Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} for which k is the maximal number of initial odd entries (0 <= k <= ceiling(n/2)). 3
0, 1, 1, 1, 2, 2, 2, 12, 8, 4, 48, 36, 24, 12, 360, 216, 108, 36, 2160, 1440, 864, 432, 144, 20160, 11520, 5760, 2304, 576, 161280, 100800, 57600, 28800, 11520, 2880, 1814400, 1008000, 504000, 216000, 72000, 14400, 18144000, 10886400, 6048000, 3024000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Sum of entries in row n is n! (A000142).

Row n has 1 + ceiling(n/2) entries.

T(n,0) = A052591(n-1).

Sum_{k=0..ceiling(n/2)} k*T(n,k) = A152663(n).

LINKS

Table of n, a(n) for n=1..44.

FORMULA

T(2n+1,k) = n*k!*(2n-k)!*binomial(n+1,k) (n>= 1);

T(2n,k) = n*k!*(2n-1-k)!*binomial(n,k).

EXAMPLE

T(3,0)=2 because we have 213 and 231.

T(4,2)=4 because we have 1324, 1342, 3124 and 3142.

Triangle starts:

    0,   1;

    1,   1;

    2,   2,   2;

   12,   8,   4;

   48,  36,  24,  12;

  360, 216, 108,  36;

MAPLE

T := proc (n, k) if n = 1 and k = 0 then 0 elif n = 1 and k = 1 then 1 elif `mod`(n, 2) = 1 then (1/2)*(n-1)*binomial((1/2)*n+1/2, k)*factorial(k)*factorial(n-1-k) else (1/2)*n*binomial((1/2)*n, k)*factorial(k)*factorial(n-1-k) end if end proc: for n to 11 do seq(T(n, k), k = 0 .. ceil((1/2)*n)) end do; # yields sequence in triangular form

CROSSREFS

Cf. A000142, A052591, A152663, A152664.

Sequence in context: A121223 A327559 A139518 * A135322 A106541 A077945

Adjacent sequences:  A152659 A152660 A152661 * A152663 A152664 A152665

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, Dec 13 2008

STATUS

approved

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Last modified December 7 00:16 EST 2019. Contains 329812 sequences. (Running on oeis4.)