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%I #11 Oct 10 2016 04:19:47
%S 1,0,1,0,0,1,0,1,0,1,0,2,4,0,1,0,9,16,9,0,1,0,44,144,54,16,0,1,0,265,
%T 1408,729,128,25,0,1,0,1854,16960,10692,2304,250,36,0,1,0,14833,
%U 237312,193185,45056,5625,432,49,0,1
%N Triangle read by rows, T(n,k) = k^(n-k)*(n-k)!*Sum_{j=0..n-k}(-1)^j/j! for 0<=k<=n.
%F T(n,k) = k^(n-k)*Gamma(1+n-k,-1)/exp(1).
%e Triangle starts:
%e 1;
%e 0, 1;
%e 0, 0, 1;
%e 0, 1, 0, 1;
%e 0, 2, 4, 0, 1;
%e 0, 9, 16, 9, 0, 1;
%e 0, 44, 144, 54, 16, 0, 1;
%e 0, 265, 1408, 729, 128, 25, 0, 1;
%e 0, 1854, 16960, 10692, 2304, 250, 36, 0, 1;
%p T := (n,k) -> A000166(n-k)*k^(n-k): for n from 0 to 9 do seq(T(n,k), k=0..n) od;
%t Table[If[n-k == 0, 1, k^(n-k) Subfactorial[n-k]], {n, 0, 10}, {k,0,n}] // Flatten
%Y Cf. A000166, A277004.
%K nonn,tabl
%O 0,12
%A _Peter Luschny_, Oct 10 2016
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