OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
a(16*n+5) = a(16*n+7) = a(16*n+8) = a(16*n+12) = a(16*n+13) = a(16*n+15) = 0.
a(2*n+1) = 2*A034950(n).
Expansion of (eta(q^2)*eta(q^4))^3/(eta(q)^2*eta(q^16)) in powers of q.
Euler transform of period-16 sequence [2,-1,2,-4,2,-1,2,-4,2,-1,2,-4,2,-1,2,-3,...].
Expansion of phi(q)phi(q^2)phi(-q^8) in powers of q where phi() is a Ramanujan theta function.
G.f.: Product_{k>0} (1+x^k)^2*(1-x^(2k))*(1-x^(4k))^2/((1+x^(4k))*(1+x^(8k))). - Michael Somos, Feb 16 2006
MATHEMATICA
a[n_]:= SeriesCoefficient[EllipticTheta[3, 0, q]*EllipticTheta[3, 0, q^2]* EllipticTheta[3, 0, -q^8], {q, 0, n}]; Table[a[n], {n, 0, 50}] (* or *)
eta[q_] := q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[ (eta[q^2]*eta[q^4])^3/(eta[q]^2*eta[q^16]), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Feb 11 2018 *)
PROG
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x^2+A)*eta(x^4+A))^3/(eta(x+A)^2*eta(x^16+A)), n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Feb 28 2003
STATUS
approved