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A230280
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Expansion of q^(-1/3) * eta(q)^4 * eta(q^2)^2 in powers of q.
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3
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1, -4, 0, 16, -10, -16, 0, 0, 39, 0, 0, -32, -70, 64, 0, 0, 49, 40, 0, -80, -22, -64, 0, 0, 110, 0, 0, 160, -128, 0, 0, 0, -130, -156, 0, 112, 182, 0, 0, 0, 121, 0, 0, -160, 0, -128, 0, 0, -320, 280, 0, 0, 170, 256, 0, 0, -69, 0, 0, -320, 38, 0, 0, 0, -190
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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Expansion of psi(x) * f(-x)^5 = phi(-x)^2 * f(-x^2)^4 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)^4 * (1 - x^(2*k))^2.
a(4*n + 2) = a(8*n + 7) = 0. a(n) = A230277(3*n + 1).
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EXAMPLE
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G.f. = 1 - 4*x + 16*x^3 - 10*x^4 - 16*x^5 + 39*x^8 - 32*x^11 + ...
G.f. = q - 4*q^4 + 16*q^10 - 10*q^13 - 16*q^16 + 39*q^25 - 32*q^34 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ x]^4 QPochhammer[ x^2]^2, {x, 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 + A)^4 * eta(x^2 + A)^2, n))};
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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