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Triangle read by rows: binomial transform of a diagonalized matrix of A026741.
1

%I #3 Mar 03 2013 14:27:44

%S 1,1,1,1,2,3,1,3,9,2,1,4,18,8,5,1,5,30,20,25,3,1,6,45,40,75,18,7,1,7,

%T 63,70,175,63,49,4,1,8,84,112,350,168,196,32,9,1,9,108,168,630,378,

%U 588,144,81,5,1,10,135,240,1050,756,1470,480,405,50,11,1,11,165,330,1650,1386

%N Triangle read by rows: binomial transform of a diagonalized matrix of A026741.

%C Row sums = A084860: (1, 2, 6, 15, 36, 84, 192,...).

%F Let X = a diagonalized matrix of A026741: [1; 0,1; 0,0,3; 0,0,0,2;], where the first few nonzero terms of A026741 are (1, 1, 3, 2, 5, 3, 7,...). The triangle = A007318 * X.

%e First few rows of the triangle are:

%e 1;

%e 1, 1;

%e 1, 2, 3;

%e 1, 3, 9, 2;

%e 1, 4, 18, 8, 5;

%e 1, 5, 30, 20, 25, 3;

%e 1, 6, 45, 40, 75, 18, 7;

%e 1, 7, 63, 70, 175, 63, 49, 4;

%e ...

%Y Cf. A026741, A084860.

%K nonn,tabl

%O 1,5

%A _Gary W. Adamson_ and _Roger L. Bagula_, Apr 27 2008