A291378 Expansion of the series reversion of -1 + 1/(1 - x/(1 - x/(1 - x^2/(1 - x^2/(1 - x^3/(1 - x^3/(1 - ...))))))), a continued fraction.

1, -2, 4, -9, 24, -74, 251, -902, 3359, -12802, 49588, -194445, 770099, -3076129, 12380317, -50162386, 204475572, -838014584, 3451174777, -14274905490, 59276495017, -247019567936, 1032709501505, -4330122550717, 18204993223606, -76728300335664, 324125242867935, -1372110743864550

Offset: 1

Author

Ilya Gutkovskiy, Aug 23 2017

Keywords

• sign

Comments

Reversion of g.f. for A006958.

Links

• N. J. A. Sloane, Transforms
• Eric Weisstein's World of Mathematics, Series Reversion
• Index entries for reversions of series

Crossrefs

Cf. A006958.

Programs

Mathematica

Rest[CoefficientList[InverseSeries[Series[-1 + 1/(1 + ContinuedFractionK[-x^Floor[(i + 1)/2], 1, {i, 1, nmax}]), {x, 0, 28}], x], x]]

Formula

G.f. A(x) satisfies: -1 + 1/(1 - A(x)/(1 - A(x)/(1 - A(x)^2/(1 - A(x)^2/(1 - A(x)^3/(1 - A(x)^3/(1 - ...))))))) = x.

a(n) ~ (-1)^(n+1) * c * d^n / n^(3/2), where d = 4.473956977950366804747779231113352537187229544... and c = 0.1202474525564857621186593278823505223773725... - Vaclav Kotesovec, May 07 2024