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%I #22 Jun 02 2018 13:06:17
%S 1,1,0,1,1,-1,1,2,1,0,1,3,7,2,1,1,4,17,40,7,0,1,5,31,150,313,33,-1,1,
%T 6,49,368,1783,3090,191,0,1,7,71,730,5857,26595,36767,1304,1,1,8,97,
%U 1272,14551,116772,476927,511648,10241,0,1,9,127,2030,30457,363045,2796671,9988872,8149601,90865,-1
%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where A(n,k) is Sum_{j=0..floor(n/2)} ((n-j)!/j!)*binomial(n-j,j)*k^(n-2*j)*(-1)^j.
%H Seiichi Manyama, <a href="/A305466/b305466.txt">Antidiagonals n = 0..139, flattened</a>
%F A(n,k) = k*n*A(n-1,k) - A(n-2,k) for n>1.
%e Square array begins:
%e 1, 1, 1, 1, 1, 1, ...
%e 0, 1, 2, 3, 4, 5, ...
%e -1, 1, 7, 17, 31, 49, ...
%e 0, 2, 40, 150, 368, 730, ...
%e 1, 7, 313, 1783, 5857, 14551, ...
%Y Columns k=0-3 give A056594, A058797, A093985(n-1), A305471.
%Y Rows n=0-2 give A000012, A001477, A056220.
%Y Main diagonal gives A305467.
%Y Cf. A305401.
%K sign,tabl
%O 0,8
%A _Seiichi Manyama_, Jun 02 2018
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