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A213641 E.g.f. satisfies: A(x) = 1 - log(1 - x^2*A(x)^2) / x. 3
1, 1, 4, 33, 408, 6760, 140880, 3543120, 104469120, 3535037856, 135053291520, 5750579640960, 270067321117440, 13868724577593600, 773138898730598400, 46500352460941579200, 3001412657729335449600, 206946807350480534937600, 15180752044039172426035200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..18.

FORMULA

E.g.f. satisfies: A(x + log(1-x^2)) = x/(x + log(1-x^2)).

E.g.f.: A(x) = (1/x)*Series_Reversion(x + log(1-x^2)).

a(n) = A213640(n+1)/(n+1).

EXAMPLE

E.g.f.: A(x) = 1 + x + 4*x^2/2! + 33*x^3/3! + 408*x^4/4! + 6760*x^5/5! +...

Related expansions:

A(x)^2 = 1 + 2*x + 10*x^2/2! + 90*x^3/3! + 1176*x^4/4! + 20240*x^5/5! +...

-log(1 - x^2*A(x)^2)/x = x + 4*x^2/2! + 33*x^3/3! + 408*x^4/4! +...

A(x + log(1-x^2)) = 1 + x + 2*x^2/2! + 9*x^3/3! + 48*x^4/4! + 340*x^5/5! +...

PROG

(PARI) {a(n)=n!*polcoeff((1/x)*serreverse(x+log(1-x^2 +x^2*O(x^n))), n)}

for(n=0, 25, print1(a(n), ", "))

CROSSREFS

Cf. A213640, A218653, A200320.

Sequence in context: A331794 A156132 A215364 * A111534 A162655 A216135

Adjacent sequences:  A213638 A213639 A213640 * A213642 A213643 A213644

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 17 2012

STATUS

approved

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Last modified May 31 10:42 EDT 2020. Contains 334748 sequences. (Running on oeis4.)