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%I #19 Mar 05 2019 01:53:38
%S 1,1,-1,1,-1,0,1,-1,-1,0,1,-1,-3,-3,0,1,-1,-7,-29,-13,0,1,-1,-15,-201,
%T -499,-71,0,1,-1,-31,-1265,-13351,-13101,-461,0,1,-1,-63,-7713,
%U -328975,-1697705,-486131,-3447,0,1,-1,-127,-46529,-7946143,-206659569,-369575303,-24266797,-29093,0
%N Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of 1/(Sum_{j>=0} (j!)^k * x^j).
%H Seiichi Manyama, <a href="/A306629/b306629.txt">Antidiagonals n = 0..59, flattened</a>
%F A(0,k) = 1 and A(n,k) = -Sum_{j=1..n} (j!)^k * A(n-j,k) for n > 0.
%e Square array begins:
%e 1, 1, 1, 1, 1, ...
%e -1, -1, -1, -1, -1, ...
%e 0, -1, -3, -7, -15, ...
%e 0, -3, -29, -201, -1265, ...
%e 0, -13, -499, -13351, -328975, ...
%e 0, -71, -13101, -1697705, -206659569, ...
%e 0, -461, -486131, -369575303, -268312660751, ...
%Y Columns 1-3 give A167894, A113871, A316862.
%Y Rows 0-2 give A000012, (-1)*A000012, (-1)*A000225.
%Y Main diagonal gives A306630.
%K sign,tabl
%O 0,13
%A _Seiichi Manyama_, Mar 02 2019
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