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%I #10 Jan 28 2019 23:51:03
%S 1,1,-2,1,-2,-3,1,-2,-3,-5,1,-2,-3,-7,1,-2,-3,-5,1,-2,-3,-11,1,-2,-3,
%T -5,-7,-13,1,-2,-3,-1,-2,-3,-5,-17
%N Irregular table of negated A080092 and a leading column of 1's.
%C The von Staudt-Clausen decomposition of nonzero Bernoulli numbers (see A164555 and A006954) states B(0)=1, B(1) = 1/2 = 1-1/2, B(2) = 1/6 = 1-1/2-1/3, B(4) = -1/30 = 1-1/2-1/3-1/5 etc.
%C We consider the denominators of the fractions in these sums, one sum per row. The first term in the sums is essentially the sequence of two 1's followed by A000146; this contributes a first column to this sequence here compared with table A080092.
%H Eric Weisstein, <a href="http://mathworld.wolfram.com/vonStaudt-ClausenTheorem.html">von Staudt-Clausen Theorem</a>, MathWorld.
%e 1;
%e 1, -2;
%e 1, -2, -3;
%e 1, -2, -3, -5;
%e 1, -2, -3, -7;
%e 1, -2, -3, -5;
%e 1, -2, -3, -11;
%e 1, -2, -3, -5, -7, -13;
%e 1, -2, -3;
%Y Cf. A046886 (row lengths minus 1), A000146.
%K tabf,less,sign
%O 0,3
%A _Paul Curtz_, Sep 29 2009
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