OFFSET
0,2
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 eta(q)^10 / eta(q^5)^2 in powers of q.
Euler transform of period 5 sequence [-10, -10, -10, -10, -8, ...].
Given g.f. A(q), then 0 = f(A(q), A(q^2), A(q^4)) where f(u, v, w) = (v^3 + u^2*w + 16*u*w^2)^2 - 4*u*w * (u + 2*v) * (v + 8*w) * (v^2 + 2*u*w).
G.f. is a period 1 Fourier series which satisfies f(-1 / (5 t)) = 5^5 (t/i)^4 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A243938.
Convolution square of A109064.
EXAMPLE
G.f. = 1 - 10*q + 35*q^2 - 30*q^3 - 105*q^4 + 240*q^5 - 20*q^6 - 190*q^7 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ q]^10 / QPochhammer[ q^5]^2, {q, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^10 / eta(x^5 + A)^2, n))};
(Magma) A := Basis( ModularForms(5, 4), 12); A[1] - 10*A[2] + 35*A[3];
(Sage) A = ModularForms( Gamma0(5), 4, prec=36) . basis(); A[1] - (A[2] + 25*A[0]) * 5/13;
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Jun 15 2014
STATUS
approved