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%I #6 Mar 27 2022 19:08:14
%S 1,0,1,1,0,2,0,1,0,6,1,0,2,0,24,0,1,0,6,0,120,1,0,2,0,24,0,720,0,1,0,
%T 6,0,120,0,5040,1,0,2,0,24,0,720,0,40320
%N Triangle read by rows: A128174 * A136572.
%C Row sums = A136580: 1, 1, 3, 7, 27, 127, ...
%F A128174 * A136572 Triangle, even rows = even n! interspersed with zeros. Odd n rows, = odd n! interspersed with zeros.
%F T(2*i,2*k) = (2*k)! = A010050(k). T(2*i+1,2*k+1) = (2*k+1)! = A009445(k). - _R. J. Mathar_, Jun 04 2021
%e First few rows of the triangle:
%e 1;
%e 0, 1;
%e 1, 0, 2;
%e 0, 1, 0, 6;
%e 1, 0, 2, 0, 24;
%e 0, 1, 0, 6, 0, 120;
%e 1, 0, 2, 0, 24, 0, 720;
%e ...
%Y Cf. A136580, A128174, A136572, A000142.
%K nonn,easy,tabl
%O 0,6
%A _Gary W. Adamson_, Jan 09 2008
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