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A113259
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Expansion of psi(q)^5/psi(q^5)-25q^2 psi(q)psi(q^5)^3 in powers of q where psi(q) is a Ramanujan theta function.
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1
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1, 5, -15, -10, 25, 5, 30, -30, -55, 35, -15, 60, -50, -60, 90, -10, 105, -80, -105, 100, 25, 60, -180, -110, 110, 5, 180, -100, -150, 150, 30, 160, -215, -120, 240, -30, 175, -180, -300, 120, -55, 210, -180, -210, 300, 35, 330, -230, -210, 215, -15, 160, -300, -260, 300, 60, 330, -200, -450
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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REFERENCES
| B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 249 Entry 8(iv).
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| G.f.: 1+5( Sum_{k>0} k x^k/(1+x^k) kronecker(5, k) ).
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PROG
| (PARI) a(n)=if(n<1, n==0, -5*sumdiv(n, d, d*kronecker(5, d)*(-1)^(n/d)))
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CROSSREFS
| Cf. a(n)=5*A113260(n) if n>0.
Sequence in context: A154353 A114332 A077348 * A166621 A160275 A200858
Adjacent sequences: A113256 A113257 A113258 * A113260 A113261 A113262
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Oct 20 2005
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