A246707 Expansion of phi(-q) * phi(-q^2) * phi(-q^3) * phi(-q^6) in powers of q.
1, -2, -2, 2, 6, 4, -14, 0, 6, -2, -12, -8, 42, 4, -16, -4, 6, -4, -50, 8, 36, 0, -24, 16, 42, 2, -28, 2, 48, -12, -84, -16, 6, 8, -36, 0, 150, -12, -40, -4, 36, 12, -112, -8, 72, 4, -48, 0, 42, 14, -62, 4, 84, 4, -158, 16, 48, -8, -60, -8, 252, 4, -64, 0, 6
Offset: 0
Keywords
Examples
G.f. = 1 - 2*q - 2*q^2 + 2*q^3 + 6*q^4 + 4*q^5 - 14*q^6 + 6*q^8 - 2*q^9 + ...
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
Programs
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Magma
A := Basis( ModularForms( Gamma0(24), 2), 26); A[1] - 2*A[2] - 2*A[3] + 2*A[4] + 6*A[5] + 4*A[6] - 14*A[7] + 6*A[8];
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Mathematica
eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[eta[q]^2* eta[q^2]*eta[q^3]^2*eta[q^6]/(eta[q^4]*eta[q^12]), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Apr 18 2018 *) -
PARI
{a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^2 + A) * eta(x^3 + A)^2 * eta(x^6 + A) / (eta(x^4 + A) * eta(x^12 + A)), n))}; -
PARI
q='q+O('q^99); Vec(eta(q)^2*eta(q^2)*eta(q^3)^2*eta(q^6)/(eta(q^4)*eta(q^12))) \\ Altug Alkan, Apr 18 2018
Comments