%I A138770
%S A138770 2,4,2,12,8,4,48,36,24,12,240,192,144,96,48,1440,1200,960,720,480,240,
%T A138770 10080,8640,7200,5760,4320,2880,1440,80640,70560,60480,50400,40320,
%U A138770 30240,20160,10080,725760,645120,564480,483840,403200,322560,241920
%N 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<=n-2).
%C A138770 Sum of row n = n! = A000142(n).
%C A138770 T(n,0)=2(n-1)! (A0528489).
%C A138770 T(n,1)=A052582(n-2).
%C A138770 T(n,2)=A052609(n-2).
%C A138770 T(n,3)=12*A005990(n-3).
%C A138770 T(n,4)=48*A061206(n-5).
%C A138770 T(n,n-2)=2(n-2)! (A052849).
%C A138770 Sum(k*T(n,k),k=0..n-2)=n!(n-2)/3=A090672(n-1).
%F A138770 T(n,k)=2*(n-k-1)(n-2)!
%e A138770 T(4,2)=4 because we have 1342, 1432, 2341 and 2431.
%e A138770 Triangle starts:
%e A138770 2;
%e A138770 4,2;
%e A138770 12,8,4;
%e A138770 48,36,24,12;
%e A138770 240,192,144,96,48;
%p A138770 T:=proc(n,k) if n-2 < k then 0 else (2*n-2*k-2)*factorial(n-2) end if 
               end proc; for n from 2 to 10 do seq(T(n, k),k=0..n-2) end do; # yields 
               sequence in triangular form
%Y A138770 Cf. A000142, A052489, A052582, A052609, A005990, A061206, A052849, A090672.
%Y A138770 Sequence in context: A121799 A078034 A161795 this_sequence A137777 A006018 
               A152666
%Y A138770 Adjacent sequences: A138767 A138768 A138769 this_sequence A138771 A138772 
               A138773
%K A138770 nonn,tabl
%O A138770 2,1
%A A138770 Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 06 2008