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A187566 Let A be the infinite lower triangular Toplitz matrix with Sigma(n) in every column; and B the diagonalized, signed variant of A002040 with the rest zeros. Sequence gives the triangle in the lower half of A*B read by rows.

%I A187566 #20 Mar 30 2012 17:25:39
%S A187566 1,3,-2,4,-6,4,7,-8,12,-8,6,-14,16,-24,21,12,-12,28,-32,63,-52,8,-24,
%T A187566 24,-56,84,-156,131,15,-16,48,-48,147,-208,393,-316,13,-30,32,-96,126,
%U A187566 -364,524,-948,765,18,-26,60,-64,252,-312,917,-1264,2295,-1846
%N A187566 Let A be the infinite lower triangular Toplitz matrix with Sigma(n) in every column; and B the diagonalized, signed variant of A002040 with the rest zeros. Sequence gives the triangle in the lower half of A*B read by rows.
%C A187566 Row sums = A000041, left border = A000203, main diagonal = A002040 (signed)
%C A187566 Equivalent to the statement that Sigma(n) convolved with A002040(signed +-+-+-...) = the partition numbers; such that (1 + 3x + 4x^2 +7x^3 + ...)*(1 -2x + 4x^2 - 8x^3 + ...) = (1 + x + 2x^2 + 3x^3 + 5x^4 + 7x^5 + ...).
%C A187566 A002040 = (1, 2, 4, 8, 21, 52, 131, 316, 765,...)
%e A187566 First few rows of the triangle =
%e A187566 1
%e A187566 3, -2
%e A187566 4, -6, 4
%e A187566 7, -8, 12, -8
%e A187566 6, -14, 16, -24, 21
%e A187566 12, -12, 28, -32, 63, -52
%e A187566 8, -24, 24, -56, 84, -156, 131
%e A187566 15, -16, 48, -48, 147, -208, 393, -316
%e A187566 13, -30, 32, -96, 126, -364, 524, -948, 765
%e A187566 18, -26, 60, -64, 252, -312, 917, -1264, 2295, -1846
%e A187566 ...
%Y A187566 Cf. A002040, A000203, A000041
%K A187566 tabl,sign
%O A187566 0,2
%A A187566 _Gary W. Adamson_, Mar 18 2011