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%I #5 Sep 07 2013 13:44:13
%S 1,1,1,1,3,2,1,5,12,6,1,7,30,60,24,1,9,56,210,360,122,1,11,90,504,
%T 1680,2562,758,1,13,132,990,5040,15372,21224,5606,1,15,182,1716,11880,
%U 36364,159180,201816,47378
%N Eigentriangle, row sums = A144251 shifted, right border = A144251.
%C Right border = A144251: (1, 1, 2, 6, 24, 122, 758,...) with row sums = the same sequence shifted. Sum of n-th row terms = rightmost term of next row.
%F Eigentriangle by rows, T(n,k) = A054142(n,k) * A144251(k); were A144251 = the eiegensequence of triangle A054142.
%e First few rows of the triangle =
%e 1;
%e 1, 1;
%e 1, 3, 2;
%e 1, 5, 12, 6;
%e 1, 7, 30, 60, 24;
%e 1, 9, 56, 210, 360, 122;
%e 1, 11, 90, 504, 1680, 2562, 758;
%e 1, 13, 132, 990, 5040, 15372, 21224, 5606;
%e ...
%e The triangle is generated from A054142 and its own eigensequence, (A144251), where A054142 =
%e 1;
%e 1, 1;
%e 1, 3, 1;
%e 1, 5, 6, 1;
%e 1, 7, 15, 10, 1;
%e ...
%e The eigensequence of A054142 = A144251: (1, 1, 2, 6, 24, 122, 758, 5606,...);
%e Example: row 3 of A144252 = (1, 5, 12, 6) = termwise products of (1, 5, 6, 1) and (1, 1, 2, 6) = (1*1, 5*1, 6*2, 1*6).
%Y A144251, Cf. A054142, A125273, A085478
%K nonn,tabl
%O 0,5
%A _Gary W. Adamson_, Sep 16 2008
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