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%I #3 Mar 30 2012 17:25:32
%S 1,3,1,5,3,4,7,5,12,12,9,7,20,36,36,11,9,28,60,108,108,13,11,36,84,
%T 180,324,324,15,13,44,108,252,540,972,972,17,15,52,132,324,756,1620,
%U 2916,2916
%N Eigentriangle of A099375 (odd number subsequences decrescendo)
%C The product A099375 * (A003946 * 0^(n-k)) creates a new eigentriangle with rows = termwise product of odd descrendo terms, e.g.: (7, 5, 3, 1) and first n terms of (1, 1, 4, 12,). The resulting triangle has row sums = (1, 4, 12, 36, 108,...), right border = (1, 1, 4, 12, 36,...) and the property that sum of n-th row terms = rightmost term of next row.
%F Triangle read by rows, A099375: (1; 3,1; 5,3,1;...) * (A003946 * 0^(n-k)); 1<=k<=n. (A003946 * 0^(n-k) = an infinite lower triangular matrix with shifted A003946: (1, 1, 4, 12, 36, 108,...) in the main diagonal and the rest zeros.
%e First few rows of the triangle = 1; 3, 1; 5, 3, 4; 7, 5, 12, 12; 9, 7, 20, 36, 36; 11, 9, 28, 60, 108, 108; 13, 11, 36, 84, 180, 324, 324; ... Row 4 = termwise product of (7, 5, 3, 1) and (1, 1, 4, 12) = (7*1, 5*1, 3*4, 1*12).
%Y A099375, Cf. A003946
%K nonn,tabl
%O 1,2
%A _Gary W. Adamson_, Sep 04 2008