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A277394 Lagrange inversion, or reversion, for divided power series with odd powers only 0
1, -2, 10, 1, -280, 56, -1, 15400, -4260, 120, 126, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Coefficients for partition polynomials for compositional inversion order-by-order of odd functions, e.g.f.s, or formal Taylor series f(x) = a1 x + a3 x^3/3! + a5 x^5/5! + ... .

The compositional inverse of f(x) is g(x)

= a1^(-1) [1] x

+ a1^(-4) [-1 a3] x^3/3!

+ a1^(-7) [10 a3^2 - 1 a1 a5] x^5/5!

+ a1^(-10)[-280 a3^3 + 56 a1 a3 a5 - a1^2 a7] x^7/7!

+ a1^(-13)[15400 a3^4 - 4620 a1 a3^2 a5 + a1^2 (120 a3 a7 + 126 a5^2) - a1^3 a9]  * x^9/9! ... .

LINKS

Table of n, a(n) for n=1..12.

CROSSREFS

Cf. A133437, A134264, A134685, A133932, A145271, A176740 for other inversion formulas.

Sequence in context: A100078 A051242 A234934 * A299581 A069287 A215749

Adjacent sequences:  A277391 A277392 A277393 * A277395 A277396 A277397

KEYWORD

sign,easy,tabf

AUTHOR

Tom Copeland, Oct 12 2016

STATUS

approved

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Last modified October 24 10:03 EDT 2021. Contains 348225 sequences. (Running on oeis4.)