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A145892 Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} having k adjacent pairs of the form (even,even) (0<=k<=floor(n/2)-1). 2
1, 1, 2, 6, 12, 12, 72, 48, 144, 432, 144, 1440, 2880, 720, 2880, 17280, 17280, 2880, 43200, 172800, 129600, 17280, 86400, 864000, 1728000, 864000, 86400, 1814400, 12096000, 18144000, 7257600, 604800, 3628800, 54432000, 181440000, 181440000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row n contains floor(n/2) entries (n>=2).

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

Sum(k*T(n,k), k>=0) = A077612(n).

T(2n,k) = A134435(2n,k).

LINKS

Table of n, a(n) for n=0..35.

FORMULA

T(2n,k) = (n!)^2*C(n-1,k)*C(n+1,k+1); T(2n+1,k) = n!(n+1)! * C(n-1,k) * C(n+2,k+2).

EXAMPLE

T(4,1) = 12 because we have 1243, 1423, 1324, 1342, 3124, 3142, 2413, 4213, 2431, 4231, 3241 and 3421.

Triangle starts:

1;

1;

2;

6;

12,     12;

72,     48;

144,   432, 144;

1440, 2880, 720;

MAPLE

T:=proc(n, k) if `mod`(n, 2) = 0 then factorial((1/2)*n)^2*binomial((1/2)*n-1, k)*binomial((1/2)*n+1, k+1) else factorial((1/2)*n-1/2)*factorial((1/2)*n+1/2)*binomial((1/2)*n-3/2, k)*binomial((1/2)* n+3/2, k+2) end if end proc: 1; 1; for n from 2 to 12 do seq(T(n, k), k = 0 .. floor((1/2)*n)-1) end do; # yields sequence in triangular form

CROSSREFS

Cf. A000142, A077612, A134434, A134435, A145891.

Sequence in context: A066791 A062723 A152667 * A216429 A250178 A154712

Adjacent sequences:  A145889 A145890 A145891 * A145893 A145894 A145895

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, Nov 30 2008

STATUS

approved

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Last modified September 28 06:57 EDT 2021. Contains 347703 sequences. (Running on oeis4.)