A295268 Expansion of e.g.f. 2/(1 + sqrt(1 - 4*LambertW(x))).
1, 1, 2, 15, 104, 1445, 18144, 364651, 6761600, 176898249, 4376614400, 140703601511, 4370369292288, 166520945009965, 6235421191430144, 274675339364551875, 12046634866183798784, 602474837696641959569, 30289753591657339944960, 1696072847731424941183039
Offset: 0
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 0..379
Programs
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Maple
S:= series(2/(1 + sqrt(1 - 4*LambertW(x))), x, 31): seq(coeff(S,x,n)*n!,n=0..30); # Robert Israel, Nov 20 2017
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Mathematica
nmax = 19; CoefficientList[Series[2/(1 + Sqrt[1 - 4 LambertW[x]]), {x, 0, nmax}], x] Range[0, nmax]! nmax = 19; CoefficientList[Series[1/(1 + ContinuedFractionK[-LambertW[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]! -
PARI
x = 'x + O('x^30); Vec(serlaplace(2/(1 + sqrt(1 - 4*lambertw(x))))) \\ Michel Marcus, Nov 20 2017
Formula
E.g.f.: 1/(1 - LambertW(x)/(1 - LambertW(x)/(1 - LambertW(x)/(1 - LambertW(x)/(1 - ...))))), a continued fraction.
a(n) ~ 2^(2*n + 3/2) * n^(n-1) / (sqrt(5) * exp(5*n/4)). - Vaclav Kotesovec, Nov 19 2017