%I A144962
%S A144962 1,1,1,1,1,2,3,1,2,4,5,3,2,4,10,17,5,6,4,10,24,41,17,10,12,10,24,66,127,
%T A144962 41,34,20,30,24,66,180,365,127,82,68,50,72,66,180,522,1119,365,254,164,
%U A144962 170,120,198,180,522,1532
%N A144962 Eigentriangle, row sums = A000084
%C A144962 Row sums = A000084: (1, 2, 4, 10, 24, 66,...).
%C A144962 Right border = A000084 shifted: (1, 1, 2, 4, 10, 24,...)
%C A144962 Left border = A001572: (1, 1, 1, 3, 5, 17, 41,...).
%C A144962 A000084 = the INVERT transform of A001572.
%C A144962 Sum of n-th row terms = rightmost term of next row.
%F A144962 Triangle read by rows, T(n,k) = A001572(n-k+1) * (A000084 * 0^(n-k)), 
               1<=k<=n.
%F A144962 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 A144962 First few rows of the triangle =
%e A144962 1;
%e A144962 1, 1;
%e A144962 1, 1, 2;
%e A144962 3, 1, 2, 4;
%e A144962 5, 3, 2, 4, 10;
%e A144962 17, 5, 6, 4, 10, 24;
%e A144962 41, 17, 10, 12, 10, 24, 66;
%e A144962 127, 41, 34, 20, 30, 24, 66, 180;
%e A144962 365, 127, 82, 68, 50, 72, 66, 180, 522;
%e A144962 1119, 365, 254, 164, 170, 120, 198, 180, 522, 1532;
%e A144962 ...
%e A144962 Example: row 5 = (5, 3, 2, 4, 10) = termwise products of (5, 3, 1, 1, 
               1) and (1, 1, 2, 4, 10).
%Y A144962 A000084, Cf. A001572
%Y A144962 Sequence in context: A035459 A048232 A163256 this_sequence A166871 A152736 
               A139246
%Y A144962 Adjacent sequences: A144959 A144960 A144961 this_sequence A144963 A144964 
               A144965
%K A144962 nonn,tabl
%O A144962 1,6
%A A144962 Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 27 2008