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A143864 Eigentriangle of A055461 (square subsequences decrescendo).

%I A143864 #8 Apr 18 2013 11:25:53
%S A143864 1,4,1,9,4,5,16,9,20,18,25,16,45,72,63,36,25,80,162,252,221,49,36,125,
%T A143864 288,567,884,776,64,49,180,450,1008,1989,3104,2725,81,64,245,648,1575,
%U A143864 3536,6984,10900,9569
%N A143864 Eigentriangle of A055461 (square subsequences decrescendo).
%C A143864 Row sums A033453: (1, 5, 18, 63, 221, 776, 2725,...); the shifted right border. Sum of row n terms = rightmost term of next row.
%F A143864 A055461 (squares decrescendo triangle) * (A033453 * 0^(n-k)); 1<=k<=1; where (A033453 * 0^(n-k)) = an infinite lower triangular matrix with the INVERT transform of the squares as the main diagonal, starting: (1, 1, 5, 18, 63, 221, 776,...) and the rest zeros.
%e A143864 First few rows of the triangle =
%e A143864 1;
%e A143864 4, 1;
%e A143864 9, 4, 5;
%e A143864 16, 9, 20, 18;
%e A143864 25, 16, 45, 72, 63;
%e A143864 36, 25, 80, 162, 252, 221;
%e A143864 49, 36, 125, 288, 567, 884, 776;
%e A143864 ...
%e A143864 Row 3 = (9, 4, 5) = termwise product of (9, 4, 1) and (1, 1, 5) (9*1, 4*1, 1*5).
%Y A143864 Cf. A055461, A033453.
%K A143864 nonn,tabl
%O A143864 1,2
%A A143864 _Gary W. Adamson_, Sep 04 2008