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A285484 G.f.: 1/(1 + x/(1 + x^3/(1 + x^6/(1 + x^10/(1 + x^15/(1 + ... + x^(k*(k+1)/2)/(1 + ...))))))), a continued fraction. 1
1, -1, 1, -1, 2, -3, 4, -6, 9, -13, 18, -26, 38, -54, 77, -111, 160, -229, 328, -472, 679, -974, 1398, -2010, 2888, -4146, 5954, -8555, 12289, -17647, 25346, -36410, 52297, -75109, 107881, -154961, 222574, -319679, 459167, -659528, 947295, -1360612, 1954295, -2807031, 4031809, -5790982 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..45.

FORMULA

a(n) ~ (-1)^n * c * d^n, where d = 1.43632929358192465555987661527... and c = 0.4856490524128736949896673... - Vaclav Kotesovec, Aug 26 2017

EXAMPLE

G.f.: A(x) = 1 - x + x^2 - x^3 + 2*x^4 - 3*x^5 + 4*x^6 - 6*x^7 + 9*x^8 - 13*x^9 + ...

MATHEMATICA

nmax = 45; CoefficientList[Series[1/(1 + ContinuedFractionK[x^(k (k + 1)/2), 1, {k, 1, nmax}]), {x, 0, nmax}], x]

CROSSREFS

Cf. A000217, A002105, A206740, A285408.

Sequence in context: A050811 A076968 A238430 * A098889 A061481 A017824

Adjacent sequences:  A285481 A285482 A285483 * A285485 A285486 A285487

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Apr 19 2017

STATUS

approved

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Last modified September 20 05:34 EDT 2021. Contains 347577 sequences. (Running on oeis4.)