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%I #2 Mar 30 2012 17:25:33
%S 1,1,1,1,1,2,3,1,2,4,5,3,2,4,10,17,5,6,4,10,24,41,17,10,12,10,24,66,
%T 127,41,34,20,30,24,66,180,365,127,82,68,50,72,66,180,522,1119,365,
%U 254,164,170,120,198,180,522,1532
%N Eigentriangle, row sums = A000084
%C Row sums = A000084: (1, 2, 4, 10, 24, 66,...).
%C Right border = A000084 shifted: (1, 1, 2, 4, 10, 24,...)
%C Left border = A001572: (1, 1, 1, 3, 5, 17, 41,...).
%C A000084 = the INVERT transform of A001572.
%C Sum of n-th row terms = rightmost term of next row.
%F Triangle read by rows, T(n,k) = A001572(n-k+1) * (A000084 * 0^(n-k)), 1<=k<=n.
%F Given an A001572 "decrescendo" triangle: (1; 1,1; 1,1,1; 3,1,1,1; 5,3,1,1,1;...), where A001572 begins: (1, 1, 1, 3, 5, 17, 41, 127,...); apply termwise products of the decrescendo triangle row terms to A000084 terms: (1, 2, 4, 10, 24, 66, 180, 522,...).
%e First few rows of the triangle =
%e 1;
%e 1, 1;
%e 1, 1, 2;
%e 3, 1, 2, 4;
%e 5, 3, 2, 4, 10;
%e 17, 5, 6, 4, 10, 24;
%e 41, 17, 10, 12, 10, 24, 66;
%e 127, 41, 34, 20, 30, 24, 66, 180;
%e 365, 127, 82, 68, 50, 72, 66, 180, 522;
%e 1119, 365, 254, 164, 170, 120, 198, 180, 522, 1532;
%e ...
%e Example: row 5 = (5, 3, 2, 4, 10) = termwise products of (5, 3, 1, 1, 1) and (1, 1, 2, 4, 10).
%Y A000084, Cf. A001572
%K nonn,tabl
%O 1,6
%A _Gary W. Adamson_, Sep 27 2008
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