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

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..379

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

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

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]!

Prog

(PARI) x = 'x + O('x^30); Vec(serlaplace(2/(1 + sqrt(1 - 4*lambertw(x))))) \\ Michel Marcus, Nov 20 2017

Crossrefs

Cf. A000108, A180680, A277184, A295267.

Sequence in context: A006675 A215643 A332048 * A037524 A037733 A308938

Adjacent sequences: A295265 A295266 A295267 * A295269 A295270 A295271

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 19 2017

Status

approved