login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A152664 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 even entries (0 <= k <= floor(n/2)). 3
1, 1, 1, 4, 2, 12, 8, 4, 72, 36, 12, 360, 216, 108, 36, 2880, 1440, 576, 144, 20160, 11520, 5760, 2304, 576, 201600, 100800, 43200, 14400, 2880, 1814400, 1008000, 504000, 216000, 72000, 14400, 21772800, 10886400, 4838400, 1814400, 518400, 86400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

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

T(n,0) = A052558(n-1).

Sum_{k=0..ceiling(n/2)} k*T(n,k) = A152665(n).

LINKS

Table of n, a(n) for n=1..41.

FORMULA

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

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

EXAMPLE

T(3,0)=4 because we have 123, 132, 312 and 321.

T(4,2)=4 because we have 2413, 2431, 4213 and 4231.

Triangle starts:

    1;

    1,   1;

    4,   2;

   12,   8,   4;

   72,  36,  12;

  360, 216, 108,  36;

MAPLE

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

CROSSREFS

Cf. A000142, A052558, A152662, A152665.

Sequence in context: A201825 A104007 A191441 * A167591 A227043 A143376

Adjacent sequences:  A152661 A152662 A152663 * A152665 A152666 A152667

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, Dec 13 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 26 23:05 EST 2020. Contains 331289 sequences. (Running on oeis4.)