A144254 - OEIS

%I #2 Mar 30 2012 17:25:32

%S 1,2,1,3,4,3,4,10,18,10,5,20,63,80,42,6,35,168,360,420,210,7,56,378,

%T 1200,2310,2520,1199,8,84,756,3300,9240,16380,16786,7670,9,120,1386,

%U 7920,30030,76440,125895,122720,54224,10,165,2376,17160,84084,286650

%N Eigentriangle by rows, termwise products of A078812 and its eigensequence, A125274.

%C Right border A144253 = A125274, the eigensequence of A078812: (1, 1, 3, 10, 42, 210, 1199,...).

%C Row sums = A125274 shifted.

%C Sum of row n terms = rightmost term of next row.

%F Eigensequence by rows, T(n,k) = A078812(n,k) * A125274(k).

%e First few rows of the triangle =

%e 1;

%e 2, 1;

%e 3, 4, 3;

%e 4, 10, 18, 10;

%e 5, 20, 63, 80, 42;

%e 6, 35, 168, 360, 420, 210;

%e 7, 56, 378, 1200, 2310, 2520, 1199;

%e ...

%e Triangle A078812 begins:

%e 1;

%e 2, 1;

%e 3, 4, 1;

%e 4, 10, 6, 1;

%e 5, 20, 21, 8, 1;

%e ...

%e Its eigensequence = A125274: (1, 1, 3, 10, 42, 210, 1199,...).

%e Row 3 of triangle A144253 = termwise products of (4, 10, 6, 1) and (1, 1, 3, 10) = (4*1, 10*1, 6*3, 1*10).

%Y A078812, Cf. A125274

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Sep 16 2008