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A206404
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E.g.f. A(x) satisfies: exp(-A(x)) = exp(-A(x)^2) - x, with A(0) = 0.
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4
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1, 3, 26, 364, 7074, 176108, 5348132, 191725840, 7924856460, 371061933552, 19411323110904, 1122067341369984, 71024428188382200, 4885895673623299008, 362955565203398550768, 28957167717593649778176, 2469386593299982674585744, 224154175905500071395278592
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..18.
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FORMULA
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E.g.f.: A(x) = Series_Reversion( exp(-x^2) - exp(-x) ).
a(n) ~ sqrt((1-2*s)/(2+2*s-4*s^2)) * n^(n-1) / (exp(1-s^2)-exp(1-s))^n, where s = 0.393815762008795197237... is the root of the equation exp(s^2) = 2*s*exp(s). - Vaclav Kotesovec, Jan 12 2014
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EXAMPLE
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E.g.f.: A(x) = x + 3*x^2/2! + 26*x^3/3! + 364*x^4/4! + 7074*x^5/5! +...
where A( exp(-x^2) - exp(-x) ) = x.
Related expansions:
exp(-A(x)) = 1 - x - 2*x^2/2! - 18*x^3/3! - 250*x^4/4! - 4840*x^5/5! +...
exp(-A(x)^2) = 1 - 2*x^2/2! - 18*x^3/3! - 250*x^4/4! - 4840*x^5/5! +...
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MATHEMATICA
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Rest[CoefficientList[InverseSeries[Series[Exp[-x^2] - Exp[-x], {x, 0, 20}], x], x] * Range[0, 20]!] (* Vaclav Kotesovec, Jan 12 2014 *)
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PROG
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(PARI) {a(n)=local(X=x+x*O(x^n)); if(n<1, 0, n!*polcoeff(serreverse(exp(-X^2) - exp(-X)), n))}
for(n=0, 30, print1(a(n), ", "))
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CROSSREFS
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Cf. A138014, A206401, A206402, A206403, A206405.
Sequence in context: A339298 A328269 A136046 * A262301 A317654 A143155
Adjacent sequences: A206401 A206402 A206403 * A206405 A206406 A206407
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Feb 07 2012
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STATUS
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approved
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