A002639 Numerators of expansion of Jacobi nome q in parameter m. (Formerly M5108 N2212)

0, 1, 1, 21, 31, 6257, 10293, 279025, 483127, 435506703, 776957575, 22417045555, 40784671953, 9569130097211, 17652604545791, 523910972020563, 976501268709949, 935823746406530603, 1758220447807291611

Offset

0,4

References

Guide to Tables, Math. Tables Other Aids Computation, 3 (1948), Section III, p. 234.

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).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Charles Hermite, Oeuvres.

Charles Hermite, Sur Quelques Développements En Série de la Théorie Des Fonctions Elliptiques , Oeuvres. Vol. 4, Gauthier-Villars, Paris, 1917, p. 477.

Charles Hermite, Annotated scan of a page from the Oeuvres, together with a page from Math. Tables Aids Comp., Vol. 3, 1948 that refers to it.

J. Tannery and J. Molk, Eléments de la Théorie des Fonctions Elliptiques (Vol. 4), Gauthier-Villars, Paris, 1902, p. 141.

Eric Weisstein's World of Mathematics, Nome

Robert M. Ziff, On Cardy's formula for the critical crossing probability in 2d percolation, J. Phys. A. 28, 1249-1255 (1995).

Example

q = 1/16*m + 1/32*m^2 + 21/1024*m^3 + 31/2048*m^4 + 6257/524288*m^5 + ...

Mathematica

Numerator[ CoefficientList[ Series[ EllipticNomeQ[m], {m, 0, 18}], m]] (* Jean-François Alcover, Sep 21 2011 *)

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))}

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

Keyword

nonn,nice,frac

Author

N. J. A. Sloane

Extensions

Edited by Michael Somos, Aug 09 2002

Status

approved