A165884 Irregular table of negated A080092 and a leading column of 1'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, -5, -7, -13, 1, -2, -3, -1, -2, -3, -5, -17

Offset

0,3

Comments

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.

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.

Links

Table of n, a(n) for n=0..35.

Eric Weisstein, von Staudt-Clausen Theorem, MathWorld.

Example

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, -5, -7, -13;
1, -2, -3;

Crossrefs

Cf. A046886 (row lengths minus 1), A000146.

Sequence in context: A092080 A264482 A193588 * A263939 A347499 A136311

Adjacent sequences: A165881 A165882 A165883 * A165885 A165886 A165887

Keyword

tabf,less,sign

Author

Paul Curtz, Sep 29 2009

Status

approved