A293719 Expansion of the series reversion of x/(1 - x^2/(1 - x^3/(1 - x^4/(1 - x^5/(1 - ...))))), a continued fraction.

1, 0, -1, 0, 2, -1, -5, 7, 13, -37, -27, 175, -2, -768, 521, 3120, -4457, -11394, 28363, 34269, -157108, -56124, 790091, -270661, -3638871, 3821242, 15153860, -29235087, -54470264, 182441139, 143800906, -1008933847, -16080652, 5067562024, -3456404771, -23114068193, 33623924709, 93441615451

Offset

1,5

Comments

Reversion of 1 - 1/g(x) where g(x) = g.f. for A005169.

Links

Table of n, a(n) for n=1..38.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Series Reversion

Index entries for reversions of series

Formula

G.f. A(x) satisfies: A(x)/(1 - A(x)^2/(1 - A(x)^3/(1 - A(x)^4/(1 - A(x)^5/(1 - ...))))) = x.

Mathematica

nmax = 38; Rest[CoefficientList[InverseSeries[Series[x/(1 + ContinuedFractionK[-x^k, 1, {k, 2, nmax}]), {x, 0, nmax}], x], x]]
nmax = 38; Rest[CoefficientList[InverseSeries[Series[1 - Sum[(-1)^i x^(i^2)/Product[(1 - x^j), {j, 1, i}], {i, 0, nmax}]/Sum[(-1)^i x^(i (i + 1))/Product[(1 - x^j), {j, 1, i}], {i, 0, nmax}], {x, 0, nmax}], x], x]]

Crossrefs

Cf. A005169, A291148, A291377.

Sequence in context: A227048 A139133 A183946 * A291377 A005297 A014551

Adjacent sequences: A293716 A293717 A293718 * A293720 A293721 A293722

Keyword

sign

Author

Ilya Gutkovskiy, Oct 15 2017

Status

approved