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A230278
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Expansion of q^(-2/3) * eta(q^2)^10 / eta(q)^4 in powers of q.
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2
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1, 4, 4, 0, 0, -8, -16, 0, -10, -20, 16, 0, 0, 40, 0, 0, 39, 28, 0, 0, 0, -40, 32, 0, -70, 0, -64, 0, 0, -80, 0, 0, 49, -20, -40, 0, 0, 112, 80, 0, -22, 56, 64, 0, 0, 88, 0, 0, 110, -140, 0, 0, 0, 0, -160, 0, -128, 52, 0, 0, 0, -280, 0, 0, -130, 28, 156, 0, 0
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OFFSET
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0,2
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COMMENTS
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Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
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LINKS
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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
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FORMULA
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Expansion of psi(x^2)^2 * f(x)^4 = phi(x)^2 * f(-x^4)^4 = psi(x)^4 * f(-x^2)^2 in powers of x where phi(), psi(), f() are Ramanujan theta functions.
Euler transform of period 2 sequence [ 4, -6, ...].
G.f.: Product_{k>0} (1 - x^k)^6 * (1 + x^k)^10.
a(4*n + 3) = a(8*n + 4) = 0. 2 * a(n) = A230277(3*n + 2).
Convolution square of A113277.
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EXAMPLE
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G.f. = 1 + 4*x + 4*x^2 - 8*x^5 - 16*x^6 - 10*x^8 - 20*x^9 + 16*x^10 + ...
G.f. = q^2 + 4*q^5 + 4*q^8 - 8*q^17 - 16*q^20 - 10*q^26 - 20*q^29 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ q^2]^10 / QPochhammer[ q]^4, {q, 0, n}]
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PROG
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^10 / eta(x + A)^4, n))}
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CROSSREFS
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Cf. A113277, A230277.
Sequence in context: A291696 A291649 A216060 * A190113 A165727 A284609
Adjacent sequences: A230275 A230276 A230277 * A230279 A230280 A230281
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Oct 15 2013
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STATUS
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approved
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