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A002639
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Numerators of expansion of Jacobi nome q in parameter m.
(Formerly M5108 N2212)
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4
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0, 1, 1, 21, 31, 6257, 10293, 279025, 483127, 435506703, 776957575, 22417045555, 40784671953, 9569130097211, 17652604545791, 523910972020563, 976501268709949, 935823746406530603, 1758220447807291611
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| Guide to Tables, Math. Tables Other Aids Computation, 3 (1948), Section III, p. 234.
C. Hermite, Oeuvres. Vol. 4, Gauthier-Villars, Paris, 1917, p. 477.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Robert M. Ziff, "On Cardy's formula for the critical crossing probability in 2d percolation," J. Phys. A. 28, 1249-1255 (1995).
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LINKS
| C. Hermite, Oeuvres.
J. Tannery and J. Molk, El\'{e}ments de la Th\'{e}orie des Fonctions Elliptiques (Vol. 4), Gauthier-Villars, Paris, 1902, p. 141.
Eric Weisstein's World of Mathematics, Nome
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EXAMPLE
| q = 1/16*m + 1/32*m^2 + 21/1024*m^3 + 31/2048*m^4 + 6257/524288*m^5 + ...
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MATHEMATICA
| Numerator[ CoefficientList[ Series[ EllipticNomeQ[m], {m, 0, 18}], m]] (* From Jean-François Alcover, Sep 21 2011 *)
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PROG
| (PARI) {a(n) = if( n<1, 0, numerator( polcoeff( serreverse( x * prod(k=1, n, (1 + x^k)^(-1)^k, 1 +x * O(x^n))^8), n) / 4^n))}
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CROSSREFS
| Cf. A119349 (denominators), A002103 (where there are further references), A005797.
Sequence in context: A068671 A166668 A019423 * A054282 A095994 A168001
Adjacent sequences: A002636 A002637 A002638 * A002640 A002641 A002642
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KEYWORD
| nonn,nice,frac
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Edited by Michael Somos, Aug 09, 2002
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