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A051273
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Expansion of q^(-1/3)b(q)c(q)/a(q)^2 in powers of q where a(q),b(q),c(q) are the three cubic AGM analog functions described by Borwein.
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0
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3, -42, 393, -3240, 24999, -184740, 1325679, -9312408, 64364025, -439225086, 2966629452, -19868187384, 132119675241, -873278632080, 5742216378024, -37587341460600, 245063740036086, -1592173816624290, 10311978807488160
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Coefficients in a certain q-series associated with a failed attempt to explain a mysterious entry in a Ramanujan notebook.
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REFERENCES
| B. C. Berndt, Ramanujan's Notebooks Part V, Springer-Verlag, see p. 179, Eq. 13.23.
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FORMULA
| Expansion of 3*(eta(q)*eta(q^3))^2/(theta[A_2](q)^2*q^(1/3)) in powers of q.
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PROG
| (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( 3*(eta(x+A)*eta(x^3+A)^2/(eta(x+A)^3+9*x*eta(x^9+A)^3))^2, n))} /* Michael Somos Aug 07 2006 */
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CROSSREFS
| Cf. A004016.
Sequence in context: A157537 A114943 A119577 * A160873 A084512 A084522
Adjacent sequences: A051270 A051271 A051272 * A051274 A051275 A051276
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected and extended by Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 15 2000
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