A285630 Expansion of r(q)^5 / r(q^5) in powers of q where r() is the Rogers-Ramanujan continued fraction.

1, -5, 15, -30, 40, -25, -35, 140, -250, 285, -150, -210, 740, -1230, 1330, -675, -880, 3015, -4830, 5025, -2450, -3135, 10380, -16180, 16450, -7875, -9785, 31850, -48720, 48600, -22800, -27985, 89465, -134760, 132530, -61400, -74205, 234515, -349000, 339145

Offset

0,2

Comments

G.f. A(q) satisfies: A(q) = u^5 / v = (v^4 - 3*v^3 + 4*v^2 - 2*v + 1) / (v^4 + 2*v^3 + 4*v^2 + 3*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): A285349 (k=2), A285628 (k=3), A285629 (k=4), this sequence (k=5).

Cf. A078905 (u^5), A229793 (1 / u^5), A285585, A285587.

Sequence in context: A212871 A188350 A268222 * A078905 A059160 A319930

Adjacent sequences: A285627 A285628 A285629 * A285631 A285632 A285633

Keyword

sign

Author

Seiichi Manyama, Apr 22 2017

Status

approved