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A144029 Eigentriangle by rows, A055615(n-k+1)*A144028(k-1); 1<=k<=n.

%I A144029 #8 Oct 05 2015 03:00:47
%S A144029 1,-2,1,-3,-2,-1,0,-3,2,-6,-5,0,3,12,-7,6,-5,0,18,14,3,-7,6,5,0,21,-6,
%T A144029 36,0,-7,-6,30,0,-9,-72,55,0,0,7,-36,35,0,-108,-110,-9,10,0,0,42,-42,
%U A144029 -15,0,-165,18,-221,-11,10,0,0,49,18,-180,0,27,442,-373,0,-11,-10,0,0,-21,216,-275,0,663,746,-18
%N A144029 Eigentriangle by rows, A055615(n-k+1)*A144028(k-1); 1<=k<=n.
%C A144029 Row sums = A144028. Right border = A144028 shifted.
%C A144029 Left border = A055615, n*mu(n).
%C A144029 Sum of n-th row terms = rightmost term of next row.
%F A144029 Eigentriangle by rows, A055615(n-k+1)*A144028(k-1); 1<=k<=n.
%e A144029 First few rows of the triangle =
%e A144029 1;
%e A144029 -2, 1;
%e A144029 -3, -2, -1;
%e A144029 0, -3, 2, -6;
%e A144029 -5, 0, 3, 12, -7;
%e A144029 6, -5, 0, 18, 14, 3;
%e A144029 -7, 6, 5, 0, 21, -6, 36;
%e A144029 0, -7, -6, 30, 0, -9, -72, 55;
%e A144029 0, 0, 7, -36, 35, 0, -108, -110, -9;
%e A144029 10, 0, 0, 42, -42, -15, 0, -165, 18, -221;
%e A144029 ...
%e A144029 Row 4 = (0, -3, 2, -6) = termwise products of (0, -3, -2, 1) and (1, 1, -1, -6) = (0*1, -3*1, -2*-1, 1*(-6)). (0, -3, -2, 1) = the first 4 terms of A055615, n*mu(n), reversed.
%e A144029 (1, 1, -1, 6) = the first 4 terms A144028, shifted.
%p A144029 read("transforms");
%p A144029 A055615 := proc(n) n*numtheory[mobius](n) ; end proc:
%p A144029 A144028 :=proc(n) if n = 0 then 1; else L := [seq(A055615(i),i=1..n+2)] ; INVERT(L) ; op(n,%) ; end if; end proc:
%p A144029 A144029 := proc(n,k) A055615(n-k+1)*A144028(k-1) ; end proc: # _R. J. Mathar_, Jan 27 2011
%Y A144029 Cf. A055615, A144028.
%K A144029 tabl,sign
%O A144029 1,2
%A A144029 _Gary W. Adamson_, Sep 07 2008
%E A144029 Entries corrected starting from row 10. - _R. J. Mathar_, Jan 27 2011