cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A055102 Expansion of cube of continued fraction 1/ ( 1+q/ ( 1+q^2/ ( 1+q^3/ ( 1+q^4/... )))).

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%I A055102 #24 Jul 29 2024 06:16:20
%S A055102 1,-3,6,-7,3,6,-17,24,-21,6,21,-54,77,-72,24,64,-159,216,-190,57,159,
%T A055102 -392,534,-468,144,381,-924,1220,-1044,312,833,-1992,2625,-2244,669,
%U A055102 1746,-4138,5382,-4530,1332,3474,-8184,10591,-8886,2607,6724,-15711
%N A055102 Expansion of cube of continued fraction 1/ ( 1+q/ ( 1+q^2/ ( 1+q^3/ ( 1+q^4/... )))).
%H A055102 Seiichi Manyama, <a href="/A055102/b055102.txt">Table of n, a(n) for n = 0..10000</a>
%H A055102 R. P. Agarwal, <a href="https://www.ias.ac.in/article/fulltext/pmsc/103/03/0269-0293">Lambert series and Ramanujan</a>, Prod. Indian Acad. Sci. (Math. Sci.), v. 103, n. 3, 1993, pp. 269-293. see p. 282.
%H A055102 G. E. Andrews, <a href="http://www.jstor.org/stable/2974472">Simplicity and surprise in Ramanujan's "Lost" Notebook</a>, Amer. Math. Monthly, 104 (No. 10, Dec. 1997), 918-925.
%F A055102 a(0) = 1, a(n) = -(3/n)*Sum_{k=1..n} A109091(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Apr 16 2017
%F A055102 G.f.: ( Sum_{k in Z} x^(2*k) / (1 - x^(5*k+2)) ) / ( Sum_{k in Z} x^k / (1 - x^(5*k+1)) ). - _Seiichi Manyama_, Jul 29 2024
%Y A055102 Product_{k>0} ((1-x^{5k-1}) * (1-x^{5k-4})/((1-x^{5k-2}) * (1-x^{5k-3})))^m: A285444 (m=-4), A285443 (m=-3), A285442 (m=-2), A003823 (m=-1), A007325 (m=1), A055101 (m=2), this sequence (m=3), A055103 (m=4).
%Y A055102 Cf. A109091, A340455, A340456.
%K A055102 sign,easy
%O A055102 0,2
%A A055102 _N. J. A. Sloane_, Jun 14 2000
%E A055102 More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 20 2000