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A295238
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Expansion of e.g.f. 2/(1 + sqrt(1 - 4*x*exp(x))).
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2
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1, 1, 6, 57, 796, 14785, 344046, 9640225, 316255416, 11896233345, 504918768250, 23874754106401, 1244712973780068, 70940791877082049, 4388291507415513894, 292823509879910802465, 20966854494419642792176, 1603540841320336494905089, 130464295561360336835272050
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OFFSET
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0,3
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COMMENTS
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Inverse binomial transform of A194471.
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LINKS
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Table of n, a(n) for n=0..18.
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FORMULA
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E.g.f.: 1/(1 - x*exp(x)/(1 - x*exp(x)/(1 - x*exp(x)/(1 - x*exp(x)/(1 - ...))))), a continued fraction.
a(n) ~ sqrt(2*(1 + LambertW(1/4))) * n^(n-1) / ((LambertW(1/4))^n * exp(n)). - Vaclav Kotesovec, Nov 18 2017
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MAPLE
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a:=series(2/(1+sqrt(1-4*x*exp(x))), x=0, 19): seq(n!*coeff(a, x, n), n=0..18); # Paolo P. Lava, Mar 27 2019
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MATHEMATICA
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nmax = 18; CoefficientList[Series[2/(1 + Sqrt[1 - 4 x Exp[x]]), {x, 0, nmax}], x] Range[0, nmax]!
nmax = 18; CoefficientList[Series[1/(1 + ContinuedFractionK[-x Exp[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[(-1)^(n - k) Binomial[n, k] k! Sum[(m + 1)^(k - m - 1) Binomial[2 m, m]/(k - m)!, {m, 0, k}], {k, 0, n}], {n, 0, 18}]
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CROSSREFS
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Cf. A000108, A006531, A052895, A194471, A295239.
Sequence in context: A032119 A294511 A242817 * A256016 A145170 A180255
Adjacent sequences: A295235 A295236 A295237 * A295239 A295240 A295241
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Nov 18 2017
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STATUS
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approved
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