%I #20 Sep 08 2022 08:45:28
%S 1,0,1,0,1,1,0,0,2,1,0,0,2,3,1,0,0,0,6,4,1,0,0,0,6,12,5,1,0,0,0,0,24,
%T 20,6,1,0,0,0,0,24,60,30,7,1,0,0,0,0,0,120,120,42,8,1,0,0,0,0,0,120,
%U 360,210,56,9,1
%N Number triangle T(n,k) = C(k,n-k)*(n-k)!.
%C Row sums are A122852.
%C Triangle T(n,k), read by rows, given by (0,1,-1,0,0,1,-1,0,0,1,-1,0,0,1,...) DELTA (1,0,0,-1,2,0,0,-2,3,0,0,-3,4,...) where DELTA is the operator defined in A084938. - _Philippe Deléham_, Dec 12 2011
%F Number triangle T(n,k)=[k<=n]*k!/(2k-n)!.
%F T(n,k) = A008279(k,n-k). - _Danny Rorabaugh_, Apr 23 2015
%e Triangle begins
%e 1,
%e 0, 1,
%e 0, 1, 1,
%e 0, 0, 2, 1,
%e 0, 0, 2, 3, 1,
%e 0, 0, 0, 6, 4, 1,
%e 0, 0, 0, 6, 12, 5, 1,
%e 0, 0, 0, 0, 24, 20, 6, 1
%t Flatten[Table[Binomial[k,n-k](n-k)!,{n,0,10},{k,0,n}]] _Harvey P. Dale_, May 16 2012
%o (Magma) /* As triangle: */ [[Binomial(k,n-k)*Factorial(n-k): k in [0..n]]: n in [0.. 7]]; // _Vincenzo Librandi_, Apr 24 2015
%Y Cf. A094587.
%K nonn,tabl,easy
%O 0,9
%A _Paul Barry_, Sep 14 2006