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A305466 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.

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