OFFSET
-1,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = -1..1000
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
G.f.: (E(q^9)*E(q^15))/(E(q^3)*E(q^45))/q where E(q) = Product_{n>=1} (1 - q^n), note that only every third term is nonzero and the zeros are omitted in this sequence, cf. the PARI/GP program. - Joerg Arndt, Apr 09 2016
a(n) ~ exp(4*Pi*sqrt(n/5)/3) / (5^(1/4)*sqrt(6)*n^(3/4)). - Vaclav Kotesovec, Apr 09 2016
Expansion of q^(1/3)*(eta(q^3)*eta(q^5)/(eta(q)*eta(q^15))) in powers of q. - G. C. Greubel, Jun 06 2018
EXAMPLE
T45b = 1/q + q^2 + 2*q^5 + 2*q^8 + 4*q^11 + 4*q^14 + 6*q^17 + 7*q^20 + ...
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[(1-x^(3*k))*(1-x^(5*k))/((1-x^k)*(1-x^(15*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 09 2016 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/3)*(eta[q^3]*eta[q^5]/(eta[q]*eta[q^15])), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 06 2018 *)
PROG
(PARI) { N=66; q='q+O('q^N); my(E=eta); Vec( (E(q^3)*E(q^5))/(E(q^1)*E(q^15))/q ) } \\ Joerg Arndt, Apr 09 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Joerg Arndt, Apr 09 2016
STATUS
approved