This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A165884 #11 Feb 16 2025 08:33:11 %S A165884 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 A165884 -5,-7,-13,1,-2,-3,-1,-2,-3,-5,-17 %N A165884 Irregular table of negated A080092 and a leading column of 1's. %C A165884 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 A165884 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 A165884 Eric Weisstein, <a href="https://mathworld.wolfram.com/vonStaudt-ClausenTheorem.html">von Staudt-Clausen Theorem</a>, MathWorld. %e A165884 1; %e A165884 1, -2; %e A165884 1, -2, -3; %e A165884 1, -2, -3, -5; %e A165884 1, -2, -3, -7; %e A165884 1, -2, -3, -5; %e A165884 1, -2, -3, -11; %e A165884 1, -2, -3, -5, -7, -13; %e A165884 1, -2, -3; %Y A165884 Cf. A046886 (row lengths minus 1), A000146. %K A165884 tabf,less,sign %O A165884 0,3 %A A165884 _Paul Curtz_, Sep 29 2009