A282611 Expansion of q^(-1/3) * c(q) * c(q^3) / 9 in powers of q where c() is a cubic AGM theta function.
0, 1, 1, 2, 1, 3, 3, 4, 4, 6, 4, 6, 3, 10, 4, 8, 7, 12, 8, 10, 7, 15, 7, 16, 9, 14, 7, 14, 12, 20, 13, 16, 13, 23, 13, 18, 12, 28, 16, 20, 16, 24, 12, 28, 17, 30, 13, 24, 20, 32, 19, 32, 16, 42, 21, 28, 19, 36, 27, 30, 21, 40, 24, 40, 19, 43, 21, 34, 28, 46
Offset: 0
Keywords
Examples
G.f. = x + x^2 + 2*x^3 + x^4 + 3*x^5 + 3*x^6 + 4*x^7 + 4*x^8 + 6*x^9 + ... G.f. = q^4 + q^7 + 2*q^10 + q^13 + 3*q^16 + 3*q^19 + 4*q^22 + 4*q^25 + ...
Links
- G. C. Greubel, Table of n, a(n) for n = 0..5000
Crossrefs
Cf. A282610.
Programs
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Magma
Basis( ModularForms( Gamma0(27), 2), 210)[5];
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Mathematica
a[ n_] := SeriesCoefficient[ x QPochhammer[ x^3]^2 QPochhammer[ x^9]^3 / QPochhammer[ x], {x, 0, n}]; -
PARI
{a(n) = if( n<1, 0, n--; my(A = x * O(x^n)); polcoeff( eta(x^3 + A)^2 * eta(x^9 + A)^3 / eta(x + A), n))};
Formula
Expansion of q^(-1/3) * eta(q^3)^2 * eta(q^9)^3 / eta(q) in powers of q.
Euler transform of period 9 sequence [1, 1, -1, 1, 1, -1, 1, 1, -4, ...].
Comments