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Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. Product_{i>0} Sum_{j=0..k} x^(j*(2*i-1))/j!.
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%I #15 Oct 10 2017 20:02:39

%S 1,1,0,1,1,0,1,1,0,0,1,1,1,6,0,1,1,1,6,24,0,1,1,1,7,24,120,0,1,1,1,7,

%T 24,180,720,0,1,1,1,7,25,180,1080,5040,0,1,1,1,7,25,180,1200,10080,

%U 80640,0,1,1,1,7,25,181,1200,10080,90720,725760,0,1,1,1,7,25

%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. Product_{i>0} Sum_{j=0..k} x^(j*(2*i-1))/j!.

%H Seiichi Manyama, <a href="/A293486/b293486.txt">Antidiagonals n = 0..139, flattened</a>

%e Square array begins:

%e 1, 1, 1, 1, 1, ...

%e 0, 1, 1, 1, 1, ...

%e 0, 0, 1, 1, 1, ...

%e 0, 6, 6, 7, 7, ...

%e 0, 24, 24, 24, 25, ...

%e 0, 120, 180, 180, 180, ...

%Y Columns k=0..3 give A000007, A293487, A293488, A293489.

%Y Rows n=0 gives A000012.

%Y Main diagonal gives A088009.

%Y Cf. A293135.

%K nonn,tabl

%O 0,14

%A _Seiichi Manyama_, Oct 10 2017