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A293719
Expansion of the series reversion of x/(1 - x^2/(1 - x^3/(1 - x^4/(1 - x^5/(1 - ...))))), a continued fraction.
0
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
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
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Oct 15 2017
STATUS
approved