A309637 G.f. satisfies A((A(x) - x)/x^2) = x, this sequence gives the coefficients at odd powers only.

1, 1, -1, 4, -24, 179, -1542, 14779, -154147, 1724785, -20499916, 256971448, -3379187370, 46424470573, -664168673391, 9868894159044, -151977742507208, 2421172940293208, -39841228681799385, 676261674504977841, -11826431722547287115, 212855326803518472588, -3938986085164523720874

Offset: 1

Author

Vladimir Reshetnikov, Aug 10 2019

Keywords

• sign

Comments

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, ...].

Examples

			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 + ...
		

Links

• Eric Weisstein's MathWorld, Series Reversion.

Crossrefs

Cf. A067145, A309254.

Programs

Mathematica

Nest[InverseSeries[#] x^2 + x &, x + O[x]^2, 30][[3, ;; ;; 2]]