

A092924


Expansion of a Schwarzian ({f_{328}, tau} / (4*Pi)^2) in powers of q^8.


0



1, 1008, 8304, 28224, 66672, 127008, 232512, 346752, 533616, 763056, 1046304, 1342656, 1866816, 2215584, 2856576, 3556224, 4269168, 4953312, 6286128, 6914880, 8400672, 9709056, 11060928, 12265344, 14941248, 15877008, 18252192, 20603520, 22935168, 24585120
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OFFSET

0,2


COMMENTS

The qseries f_{328} is the g.f. for A082303. This is given on page 274 of McKay and Sebbar along with equation (8.1) which gives an expression for the g.f. A(q) of this sequence.  Michael Somos, Aug 15 2014


LINKS

Table of n, a(n) for n=0..29.
J. McKay and A. Sebbar, Fuchsian groups, automorphic functions and Schwarzians, Math. Ann., 318 (2000), 255275.


FORMULA

Expansion of (21 * E_4(q)  16 * E_4(q^2)) / 5 in powers of q. [McKay and Sebbar, equation (8.1)]  Michael Somos, Aug 15 2014
G.f. is a period 1 Fourier series which satisfies f(1 / (4 t)) = 16 (t/i)^4 f(t) where q = exp(2 Pi i t).  Michael Somos, Aug 15 2014


EXAMPLE

G.f. = 1  1008*x + 8304*x^2  28224*x^3 + 66672*x^4  127008*x^5 + 232512*x^6 + ...
G.f. = 1  1008*q^8 + 8304*q^16  28224*q^24 + 66672*q^32  127008*q^40 + ...


PROG

(Sage) A = ModularForms( Gamma0(8), 4, prec=32) . basis(); A[1]  1008*A[2] + 8304*A[3] + 66672*A[4]; # Michael Somos, Aug 15 2014


CROSSREFS

Cf. A062248, A082303.
Sequence in context: A163557 A241932 A160451 * A187863 A145235 A210759
Adjacent sequences: A092921 A092922 A092923 * A092925 A092926 A092927


KEYWORD

sign


AUTHOR

John McKay (mckay(AT)cs.concordia.ca), Apr 18 2004


EXTENSIONS

More terms from Michael Somos, Aug 15 2014


STATUS

approved



