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%I #7 Oct 10 2016 04:19:29
%S 1,0,1,1,0,4,2,1,0,27,9,2,4,0,256,44,9,8,27,0,3125,265,44,36,54,256,0,
%T 46656,1854,265,176,243,512,3125,0,823543,14833,1854,1060,1188,2304,
%U 6250,46656,0,16777216,133496,14833,7416,7155,11264,28125,93312,823543,0,387420489
%N Triangle read by rows, T(n,k) = k^k*(n-k)!*Sum_{j=0..n-k}(-1)^j/j! for 0<=k<=n.
%F T(n,k) = k^k*Gamma(1+n-k,-1)/exp(1).
%e Triangle starts:
%e [ 1]
%e [ 0, 1]
%e [ 1, 0, 4]
%e [ 2, 1, 0, 27]
%e [ 9, 2, 4, 0, 256]
%e [ 44, 9, 8, 27, 0, 3125]
%e [ 265, 44, 36, 54, 256, 0, 46656]
%e [ 1854, 265, 176, 243, 512, 3125, 0, 823543]
%e [14833, 1854, 1060, 1188, 2304, 6250, 46656, 0, 16777216]
%p T := (n,k) -> k^k*(n-k)!*add((-1)^j/j!,j=0..n-k): seq(seq(T(n,k),k=0..n),n=0..9);
%Y Cf. T(n,0) = T(n+1,1) = A000166(n), T(n,n) = T(n+2,n) = A000312(n), A276995.
%K nonn,tabl
%O 0,6
%A _Peter Luschny_, Oct 10 2016
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