

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
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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(n1).
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!*(2nk)!*binomial(n+1,k) (n>= 1);
T(2n,k) = n*k!*(2n1k)!*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)*(n1)*binomial((1/2)*n+1/2, k)*factorial(k)*factorial(n1k) else (1/2)*n*binomial((1/2)*n, k)*factorial(k)*factorial(n1k) 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



