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 A309637 #6 Feb 16 2025 08:33:55 %S A309637 1,1,-1,4,-24,179,-1542,14779,-154147,1724785,-20499916,256971448, %T A309637 -3379187370,46424470573,-664168673391,9868894159044,-151977742507208, %U A309637 2421172940293208,-39841228681799385,676261674504977841,-11826431722547287115,212855326803518472588,-3938986085164523720874 %N A309637 G.f. satisfies A((A(x) - x)/x^2) = x, this sequence gives the coefficients at odd powers only. %C A309637 The g.f. given by A((A(x) - x)/x^2) = x generates aerated sequence [1, 0, 1, 0, -1, 0, 4, 0, -24, ...], which shifts left by 2 places under g.f. series reversion. In this it is similar to A309254, but unlike A309254 (which starts with [1, 1, ...]), this aerated sequence starts with [1, 0, ...]. %H A309637 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/SeriesReversion.html">Series Reversion</a>. %e A309637 The series reversion of x + x^3 - x^5 + 4*x^7 - 24*x^9 + ... is x - x^3 + 4*x^5 - 24*x^7 + ... %t A309637 Nest[InverseSeries[#] x^2 + x &, x + O[x]^2, 30][[3, ;; ;; 2]] %Y A309637 Cf. A067145, A309254. %K A309637 sign %O A309637 1,4 %A A309637 _Vladimir Reshetnikov_, Aug 10 2019