OFFSET
0,36
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q^(-1) * (eta(q^10) * eta(q^14) - eta(q^2) * eta(q^70)) in powers of q^2.
G.f. is a period 1 Fourier series which satisfies f(-1 / (140 t)) = 140^(1/2) (t/i) f(t) where q = exp(2 Pi i t).
EXAMPLE
G.f. = 1 - x + x^2 + x^3 - x^5 - x^6 - x^7 - x^8 - x^10 + x^12 + x^13 + ...
G.f. = q - q^3 + q^5 + q^7 - q^11 - q^13 - q^15 - q^17 - q^21 + q^25 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^5] QPochhammer[ x^7] - x QPochhammer[ x] QPochhammer[ x^35], {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^5 + A) * eta(x^7 + A) - x * eta(x + A) * eta(x^35 + A), n))};
(PARI) {a(n) = my(j=24*n+12, n1, n2, t1, t2); if( n<0, 0, n1 = sqrtint(j\7); n2 = sqrtint(j\35); sum(k = (-n1+4)\6, (n1-1)\6, if( (t1 = j-7*(6*k+1)^2)%5 ==0 && issquare( t1/5, &t2), if( t2%6 == 5, t2=-t2); m = (t2-1)/6; (-1)^(k+m))) - sum(k = (-n2+4)\6, (n2-1)\6, t1 = j-35*(6*k+1)^2; if( issquare( t1, &t2), if( t2%6 == 5, t2=-t2); m = (t2-1)/6; (-1)^(k+m))))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Oct 21 2016
STATUS
approved