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A092924 Expansion of a Schwarzian ({f_{32|8}, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The q-series f_{32|8} 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), 255-275.

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

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Last modified November 25 21:44 EST 2014. Contains 250010 sequences.