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A107034
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Expansion of f(-x) * f(-x^4) in powers of x where f() is a Ramanujan theta function.
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2
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1, -1, -1, 0, -1, 2, 1, 1, -1, 0, 1, -1, -1, -1, 0, -2, 1, 0, 0, 1, 2, -1, 0, 1, 0, 1, 0, 1, 1, -1, -3, 0, -1, 1, -1, -1, 0, 0, 0, 1, -2, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 1, 0, -1, 1, -3, 0, 1, 0, -1, -1, 0, 1, 0, 0, -2, 0, -1, -1, 0, -2, 1, 1, 0, 0, 1, 0, 0, 1
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OFFSET
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0,6
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COMMENTS
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REFERENCES
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H. Kahl, G. Koehler, Components of Hecke theta series, J. Math. Anal. Appl. 232 (1999), no. 2, 312-331, see page 320. MR1683136 (2000e:11051)
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LINKS
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FORMULA
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Expansion of f(x)^2 / chi(x)^3 = f(x)^5 / phi(x)^3 = f(-x^2)^2 / chi(x) = f(-x^2) * psi(-x) = f(-x^2)^3 / f(x) = phi(x)^2 / chi(x)^5 = psi(-x)^2 * chi(x) in powers of x where phi(), psi(), chi(), f() are Ramanujan theta functions. - Michael Somos, Jan 29 2015
Expansion of q^(-5/24) * eta(q) * eta(q^4) in powers of q.
Euler transform of period 4 sequence [-1, -1, -1, -2, ...].
G.f. Product_{k>0} (1 - x^k) * (1 - x^(4*k)).
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EXAMPLE
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G.f. = 1 - x - x^2 - x^4 + 2*x^5 + x^6 + x^7 - x^8 + x^10 - x^11 - x^12 - ...
G.f. = q^5 - q^29 - q^53 - q^101 + 2*q^125 + q^149 + q^173 - q^197 + q^245 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ x] QPochhammer[ x^4], {x, 0, n}]; (* Michael Somos, Jan 29 2015 *)
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PROG
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(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^4 + A), 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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