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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.
3

%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