%I #4 Mar 03 2013 13:49:19
%S 1,1,1,1,1,2,3,3,3,1,3,6,10,15,15,15,1,4,10,22,43,70,105,105,105,1,5,
%T 15,40,95,201,390,630,945,945,945,1,6,21,65,180,456,1066,2226,4305,
%U 6930,10395,10395,10395,1,7,28,98,308,896,2422,6028,13993,29043,56070,90090
%N Triangle read by rows, X^n * [1,0,0,0,...]; where X = a tridiagonal matrix with (1,1,1,...) in the main and subdiagonals and (1,2,3,...) in the subsubdiagonal.
%C Rightmost terms of each row form A001147: (1, 1, 3, 15, 105, 945,...).
%e First few rows of the triangle are:
%e 1;
%e 1, 1, 1;
%e 1, 2, 3, 3, 3;
%e 1, 3, 6, 10, 15, 15, 15;
%e 1, 4, 10, 22, 43, 70, 105, 105, 105;
%e 1, 5, 15, 40, 95, 201, 390, 630, 945, 945, 945;
%e 1, 6, 21, 65, 180, 456, 1066, 2226, 4305, 6930, 10395, 10395, 10395;
%e ...
%Y Cf. A140734, A140735, A001147.
%K nonn,tabl
%O 1,6
%A _Gary W. Adamson_ & _Roger L. Bagula_, May 25 2008