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%I #5 Aug 11 2019 02:34:42
%S 1,1,-1,4,-24,179,-1542,14779,-154147,1724785,-20499916,256971448,
%T -3379187370,46424470573,-664168673391,9868894159044,-151977742507208,
%U 2421172940293208,-39841228681799385,676261674504977841,-11826431722547287115,212855326803518472588,-3938986085164523720874
%N G.f. satisfies A((A(x) - x)/x^2) = x, this sequence gives the coefficients at odd powers only.
%C 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 Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/SeriesReversion.html">Series Reversion</a>.
%e 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 Nest[InverseSeries[#] x^2 + x &, x + O[x]^2, 30][[3, ;; ;; 2]]
%Y Cf. A067145, A309254.
%K sign
%O 1,4
%A _Vladimir Reshetnikov_, Aug 10 2019
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