A285585 Expansion of r(q^5) / r(q)^5 in powers of q where r() is the Rogers-Ramanujan continued fraction.

1, 5, 10, 5, -15, -25, 10, 60, 25, -110, -150, 85, 360, 155, -505, -675, 330, 1410, 555, -1925, -2450, 1210, 4920, 1930, -6275, -7875, 3710, 15000, 5720, -18575, -22800, 10735, 42310, 15960, -50605, -61400, 28280, 110610, 41100, -129570, -155250, 71060, 274320

Offset: 0

Author

Seiichi Manyama, Apr 22 2017

Keywords

• sign

Comments

G.f. A(q) satisfies: A(q) = v / u^5 = (v^4 + 2*v^3 + 4*v^2 + 3*v + 1) / (v^4 - 3*v^3 + 4*v^2 - 2*v + 1), where u = r(q) and v = r(q^5).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Bruce C. Berndt, Heng Huat Chan, Sen-Shan Huang, Soon-Yi Kang, Jaebum Sohn, and Seung Hwan Son, The Rogers-Ramanujan continued fraction, Journal of Computational and Applied Mathematics, Vol. 105, No. 1-2 (1999), 9-24.

Crossrefs

r(q^k) / r(q)^k: A285348 (k=2), A285583 (k=3), A285584 (k=4), this sequence (k=5).

Cf. A078905 (u^5), A229793 (1 / u^5), A285587, A285630.