OFFSET
0,5
COMMENTS
a(n) > 0.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction.
FORMULA
G.f.: Product_{i>=1} Product_{j>=1} (1-x^(i*(5*j-2))) * (1-x^(i*(5*j-3))) / ((1-x^(i*(5*j-1))) * (1-x^(i*(5*j-4)))).
G.f.: Product_{k>=1} (1-x^k)^(-A035187(k)).
a(n) ~ c * exp(Pi*sqrt(r*n)) / n^(3/4), where r = 4*log((1+sqrt(5))/2) / (3*sqrt(5)) = 0.2869392939760026925..., c = 0.203427046022096... - Vaclav Kotesovec, Sep 24 2019, updated May 09 2020
MATHEMATICA
nmax = 60; CoefficientList[Series[Product[QPochhammer[x^(5*j - 3)] * QPochhammer[x^(5*j - 2)]/(QPochhammer[x^(5*j - 4)] * QPochhammer[x^(5*j - 1)]), {j, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 23 2019 *)
PROG
(PARI) N=66; x='x+O('x^N); Vec(1/prod(k=1, N, (1-x^k)^sumdiv(k, d, kronecker(5, d))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 23 2019
STATUS
approved