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A291377 Expansion of the series reversion of x/(1 + x^2/(1 + x^3/(1 + x^4/(1 + x^5/(1 + ...))))), a continued fraction. 1
1, 0, 1, 0, 2, -1, 5, -7, 15, -35, 57, -155, 262, -664, 1297, -2910, 6437, -13428, 31461, -65137, 152576, -325838, 744223, -1649943, 3685869, -8376976, 18574146, -42579093, 94912298, -217177891, 489321856, -1114542791, 2535640016, -5761630456, 13184657747, -29989008137 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Reversion of g.f. (with constant term omitted) for A003823.

LINKS

Table of n, a(n) for n=1..36.

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

Rest[CoefficientList[InverseSeries[Series[ContinuedFractionK[x^i, 1, {i, 1, 36}], {x, 0, 36}], x], x]]

Rest[CoefficientList[InverseSeries[Series[-1 + QPochhammer[x^2, x^5] QPochhammer[x^3, x^5]/(QPochhammer[x, x^5] QPochhammer[x^4, x^5]), {x, 0, 36}], x], x]]

CROSSREFS

Cf. A003823.

Sequence in context: A139133 A183946 A293719 * A005297 A014551 A175002

Adjacent sequences:  A291374 A291375 A291376 * A291378 A291379 A291380

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Aug 23 2017

STATUS

approved

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Last modified August 9 18:32 EDT 2020. Contains 336326 sequences. (Running on oeis4.)