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A124840 Triangle, row sums = A008683, the Mobius sequence. 1

%I

%S 1,1,-2,1,-4,2,1,-6,6,-1,1,-8,12,-4,-2,1,-10,20,-10,-10,10,1,-12,30,

%T -20,-30,60,-30,1,-14,42,-35,-70,210,-210,76,1,-16,46,-56,-140,560,

%U -840,608,-173

%N Triangle, row sums = A008683, the Mobius sequence.

%C Cf. A124839, the inverse binomial transform of mu(n), A008683

%F Binomial transform of the diagonalized matrix using A124839; i.e. let A124839 (1, -2, 2, -1...) = the diagonal of an infinite matrix M; then the triangle (deleting the zeros) = P*M where P = Pascal's triangle as an infinite lower triangular matrix.

%e First few rows of the triangle are:

%e 1;

%e 1, -2;

%e 1, -4, 2;

%e 1, -6, 6, -1;

%e 1, -8, 12, -4, -2

%e 1, -10, 20, -10, -10, 10;

%e 1, -12, 30, -20, -30, 60, -30;

%e ...

%e E.g. mu(5) = -1 = sum of row 5 terms: (1 - 8 + 12 - 4 - 2).

%Y Cf. A124839, A008683.

%K sign,tabl

%O 1,3

%A _Gary W. Adamson_, Nov 10 2006

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Last modified September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)