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A218653 E.g.f. satisfies: A(x) = 1 + log(1 + x^2*A(x)^2)/x. 2
1, 1, 4, 27, 264, 3400, 54480, 1045800, 23412480, 599157216, 17258814720, 552733695360, 19485393903360, 749871707270400, 31283408387911680, 1406370859616923200, 67780975948945459200, 3486485719168394342400, 190644828634476331315200, 11043310871932837194977280 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

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) = A218652(n+1)/(n+1).

EXAMPLE

E.g.f: A(x) = 1 + x + 4*x^2/2! + 27*x^3/3! + 264*x^4/4! + 3400*x^5/5! +...

Related expansions:

A(x)^2 = 1 + 2*x + 10*x^2/2! + 78*x^3/3! + 840*x^4/4! + 11600*x^5/5! +...

log(1 + x^2*A(x)^2)/x = x + 4*x^2/2! + 27*x^3/3! + 264*x^4/4! + 3400*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. A218652, A213641.

Sequence in context: A301335 A177379 A052813 * A121353 A265270 A161633

Adjacent sequences:  A218650 A218651 A218652 * A218654 A218655 A218656

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 03 2012

STATUS

approved

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Last modified March 18 17:51 EDT 2019. Contains 321292 sequences. (Running on oeis4.)