OFFSET
0,23
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of sqrt((-8 - T15b(q) - T15b(q^2) + T15b(q)*T15b(q^2))/(5 + T15b(q) + T15b(q^2))) in powers of q, where T15b(q) = A058513. - G. C. Greubel, Jul 02 2018
EXAMPLE
T60d = 1/q -q -q^3 -q^13 -q^17 -q^21 -q^23 +q^29 -q^33 -q^37 +...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; B:= (eta[q]/eta[q^25]); d:= q*(eta[q^3]/eta[q^15])^2; c:= (eta[q^3]*eta[q^5]/(eta[q]* eta[q^15]))^3; T25A := B + 5/B; A:= (eta[q^3]/eta[q^75]); T15b:= Simplify[2 + (-5 + T25A*(A + 5/A))*(-B + A)*(1/(A*B))^2*(d^3/c)/q^3, q>0]; T60d:= CoefficientList[Series[(q*((-8 - T15b - (T15b /. {q -> q^2}) + T15b*(T15b /. {q -> q^2}))/(5 + T15b + (T15b /. {q -> q^2}))) + O[q]^nmax)^(1/2), {q, 0, nmax}], q]; Table[T60d[[n]], {n, 1, nmax}] (* G. C. Greubel, Jul 02 2018 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Aug 28 2005
STATUS
approved