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A291376
Expansion of the series reversion of x/(1 - 2*x/(1 - 3*x/(1 - 4*x/(1 - 5*x/(1 - ...))))), a continued fraction.
0
1, -2, -2, -14, -134, -1610, -22970, -376070, -6912590, -140545682, -3127227122, -75537934526, -1968218386646, -55032827628122, -1643983822922282, -52268580072454070, -1762720241380630430, -62864993479711480610, -2364417640569364405730, -93549390640311405418094
OFFSET
1,2
COMMENTS
Reversion of g.f. (with constant term omitted) for A000698.
LINKS
FORMULA
G.f. A(x) satisfies: A(x)/(1 - 2*A(x)/(1 - 3*A(x)/(1 - 4*A(x)/(1 - 5*A(x)/(1 - ...))))) = x.
a(n) ~ -2^(n + 1/2) * n^n / exp(n+1). - Vaclav Kotesovec, May 07 2024
MATHEMATICA
Rest[CoefficientList[InverseSeries[Series[x/(1 + ContinuedFractionK[-i x, 1, {i, 2, 20}]), {x, 0, 20}], x], x]]
Rest[CoefficientList[InverseSeries[Series[1 - 1/(1 + Sum[(2 i - 1)!! x^i, {i, 1, 20}]), {x, 0, 20}], x], x]]
CROSSREFS
Cf. A000698.
Sequence in context: A292080 A333372 A350923 * A273319 A009773 A325912
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Aug 23 2017
STATUS
approved