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Search: id:A002639
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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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+0
5
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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; listen)
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OFFSET
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0,4
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
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
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J. Tannery and J. Molk, El\'{e}ments de la Th\'{e}orie des Fonctions Elliptiques (Vol. 4), Gauthier-Villars, Paris, 1902, p. 141.
C. Hermite, Oeuvres.
Eric Weisstein's World of Mathematics, Nome
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EXAMPLE
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q = 1/16*m + 1/32*m^2 + 21/1024*m^3 + 31/2048*m^4 + 6257/524288*m^5 + ...
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PROGRAM
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(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
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Cf. A119349 (denominators), A002103 (where there are further references), A005797.
Sequence in context: A068671 A166668 A019423 this_sequence A054282 A095994 A118866
Adjacent sequences: A002636 A002637 A002638 this_sequence A002640 A002641 A002642
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KEYWORD
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nonn,nice,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Edited by Michael Somos, Aug 09, 2002
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