OFFSET
-1,4
COMMENTS
Apart from a(0) same as A034320. [Joerg Arndt, Apr 09 2016]
LINKS
G. C. Greubel, 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).
H. D. Nguyen, D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013; Mentions this sequence. - From N. J. A. Sloane, Mar 16 2014
FORMULA
G.f.: (E(q^2)*E(q^25))/(E(q)*E(q^50))/q - 1 where E(q) = prod(n>=1, 1 - q^n ). - Joerg Arndt, Apr 09 2016
a(n) ~ exp(2*Pi*sqrt(2*n)/5) / (2^(3/4) * sqrt(5) * n^(3/4)). - Vaclav Kotesovec, Sep 06 2017
EXAMPLE
T50a = 1/q + q + 2*q^2 + 2*q^3 + 3*q^4 + 4*q^5 + 5*q^6 + 6*q^7 + 8*q^8 + ...
MATHEMATICA
nmax = 60; CoefficientList[Series[-x + Product[(1 + x^k)/(1 + x^(25*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 06 2017 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[-1 + (eta[q^2]*eta[q^25])/(eta[q]*eta[q^50]), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018*)
PROG
(PARI) N=66; q='q+O('q^N); Vec( (eta(q^2)*eta(q^25))/(eta(q)*eta(q^50))/q - 1 ) \\ 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