

A138770


Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} such that there are exactly k entries between the entries 1 and 2 (n>=2, 0<=k<=n2).


3



2, 4, 2, 12, 8, 4, 48, 36, 24, 12, 240, 192, 144, 96, 48, 1440, 1200, 960, 720, 480, 240, 10080, 8640, 7200, 5760, 4320, 2880, 1440, 80640, 70560, 60480, 50400, 40320, 30240, 20160, 10080, 725760, 645120, 564480, 483840, 403200, 322560, 241920
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,1


COMMENTS

Sum of row n = n! = A000142(n).
T(n,0)=2(n1)! = A052849(n1)
T(n,1)=A052582(n2).
T(n,2)=A052609(n2).
T(n,3)=12*A005990(n3).
T(n,4)=48*A061206(n5).
T(n,n2)=2(n2)! (A052849).
Sum(k*T(n,k),k=0..n2)=n!(n2)/3=A090672(n1).
The expected value of k is (n2)/3 [From Geoffrey Critzer, Dec 19 2009]


LINKS

Table of n, a(n) for n=2..44.


FORMULA

T(n,k)=2*(nk1)(n2)!


EXAMPLE

T(4,2)=4 because we have 1342, 1432, 2341 and 2431.
Triangle starts:
2;
4,2;
12,8,4;
48,36,24,12;
240,192,144,96,48;


MAPLE

T:=proc(n, k) if n2 < k then 0 else (2*n2*k2)*factorial(n2) end if end proc; for n from 2 to 10 do seq(T(n, k), k=0..n2) end do; # yields sequence in triangular form


MATHEMATICA

Table[Table[2 (n  r) (n  2)!, {r, 1, n  1}], {n, 1, 10}] // Grid [From Geoffrey Critzer, Dec 19 2009]


CROSSREFS

Cf. A000142, A052489, A052582, A052609, A005990, A061206, A052849, A090672.
Sequence in context: A078034 A181091 A161795 * A006018 A152666 A153801
Adjacent sequences: A138767 A138768 A138769 * A138771 A138772 A138773


KEYWORD

nonn,tabl


AUTHOR

Emeric Deutsch, Apr 06 2008


STATUS

approved



