A301629 - OEIS

%I #6 Nov 04 2021 08:03:18

%S 1,-1,2,-4,8,-15,23,-14,-95,616,-2597,9280,-29971,89283,-245617,

%T 614122,-1330205,2121789,-134318,-18870272,111955244,-481559262,

%U 1783749762,-5976975892,18406561660,-52025500982,132347403714,-285820317372,421120353772,271625450178,-5772145145591

%N G.f. A(x) satisfies: A(x) = 1/(1 + x*A(x)/(1 + x^2*A(x)^2/(1 + x^3*A(x)^3/(1 + x^4*A(x)^4/(1 + ...))))), a continued fraction.

%H Vaclav Kotesovec, <a href="/A301629/b301629.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rogers-RamanujanContinuedFraction.html">Rogers-Ramanujan Continued Fraction</a>

%e G.f. A(x) = 1 - x + 2*x^2 - 4*x^3 + 8*x^4 - 15*x^5 + 23*x^6 - 14*x^7 - 95*x^8 + 616*x^9 - 2597*x^10 + ...

%e log(A(x)) = -x + 3*x^2/2 - 7*x^3/3 + 15*x^4/4 - 26*x^5/5 + 15*x^6/6 + 153*x^7/7 - 1049*x^8/8 + ... + A291651(n)*x^n/n + ...

%Y Cf. A007325, A192728, A192737, A291651, A301362, A301627.

%K sign

%O 0,3

%A _Ilya Gutkovskiy_, Mar 24 2018