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

1, -3, 6, -7, 3, 6, -17, 24, -21, 6, 21, -54, 77, -72, 24, 64, -159, 216, -190, 57, 159, -392, 534, -468, 144, 381, -924, 1220, -1044, 312, 833, -1992, 2625, -2244, 669, 1746, -4138, 5382, -4530, 1332, 3474, -8184, 10591, -8886, 2607, 6724, -15711

Offset: 0

Author

N. J. A. Sloane, Jun 14 2000

Keywords

• sign
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• R. P. Agarwal, Lambert series and Ramanujan, Prod. Indian Acad. Sci. (Math. Sci.), v. 103, n. 3, 1993, pp. 269-293. see p. 282.
• G. E. Andrews, Simplicity and surprise in Ramanujan's "Lost" Notebook, Amer. Math. Monthly, 104 (No. 10, Dec. 1997), 918-925.

Crossrefs

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).

Cf. A109091, A340455, A340456.

Formula

a(0) = 1, a(n) = -(3/n)*Sum_{k=1..n} A109091(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 16 2017

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

Extensions

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 20 2000