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Triangle read by rows: A128174 * A136572.
3

%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