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A309637
G.f. satisfies A((A(x) - x)/x^2) = x, this sequence gives the coefficients at odd powers only.
0
1, 1, -1, 4, -24, 179, -1542, 14779, -154147, 1724785, -20499916, 256971448, -3379187370, 46424470573, -664168673391, 9868894159044, -151977742507208, 2421172940293208, -39841228681799385, 676261674504977841, -11826431722547287115, 212855326803518472588, -3938986085164523720874
OFFSET
1,4
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, ...].
LINKS
Eric Weisstein's MathWorld, Series Reversion.
EXAMPLE
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 + ...
MATHEMATICA
Nest[InverseSeries[#] x^2 + x &, x + O[x]^2, 30][[3, ;; ;; 2]]
CROSSREFS
Sequence in context: A139702 A213591 A243689 * A168452 A361594 A061720
KEYWORD
sign
AUTHOR
STATUS
approved