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%I #9 May 12 2018 07:10:15
%S 1,0,1,0,1,12,0,1,60,360,0,1,252,5040,20160,0,1,1020,52920,604800,
%T 1814400,0,1,4092,506880,12640320,99792000,239500800,0,1,16380,
%U 4684680,230630400,3632428800,21794572800,43589145600,0,1,65532,42653520,3952428480
%N T(n, k) = Sum_{j=0..k} (-1)^j*binomial(2*k, j)*(k - j)^(2*n), triangle read by rows, n >= 0 and 0 <= k <= n.
%e Triangle starts:
%e [0] 1;
%e [1] 0, 1;
%e [2] 0, 1, 12;
%e [3] 0, 1, 60, 360;
%e [4] 0, 1, 252, 5040, 20160;
%e [5] 0, 1, 1020, 52920, 604800, 1814400;
%e [6] 0, 1, 4092, 506880, 12640320, 99792000, 239500800;
%e [7] 0, 1, 16380, 4684680, 230630400, 3632428800, 21794572800, 43589145600;
%p T := (n, k) -> add((-1)^j*binomial(2*k,j)*(k-j)^(2*n), j=0..k):
%p for n from 0 to 8 do seq(T(n, k), k=0..n) od;
%Y Row sums are A100872, T(n,2) = A058896, T(n,n) = A002674, T(n,n-1)= A091032.
%Y Cf. A304334, A304336.
%K nonn,tabl
%O 0,6
%A _Peter Luschny_, May 11 2018
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