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A170991 Number of genus 2, degree n, simply ramified covers of an elliptic curve. 8
2, 16, 60, 160, 360, 672, 1240, 1920, 3180, 4400, 6832, 8736, 12880, 15840, 22320, 26112, 36666, 41040, 55720, 62720, 82104, 89056, 119520, 124800, 161980, 174240, 219744, 227360, 295920, 297600, 377952, 392832, 480420, 486080, 623820, 607392, 753160, 771680, 934800, 918400, 1157184 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
The reference gives a generating function and the terms up to degree 18.
LINKS
Mike Roth and Noriko Yu, Mirror Symmetry for Elliptic Curves: The A-Model (Fermionic) Counting, Clay Mathematics Proceedings, Volume 11, 2010.
FORMULA
G.f.: (5*E_2^3 - 3*E_2*E_4 - 2*E_6)/25920, where E_k = 1 - (2*k/B_k)*Sum_{i > 0} Sum_{d dividing i} d^(k-1)*q^i is the Eisenstein series of weight k. - Robin Visser, Aug 08 2023
PROG
(Sage)
def a(n):
E2 = sum([1]+[-24*sigma(k)*x^k for k in range(1, n+1)])
E4 = sum([1]+[240*sigma(k, 3)*x^k for k in range(1, n+1)])
E6 = sum([1]+[-504*sigma(k, 5)*x^k for k in range(1, n+1)])
f = (5*E2^3 - 3*E2*E4 - 2*E6)/25920
return f.taylor(x, 0, n).coefficient(x^n) # Robin Visser, Aug 08 2023
CROSSREFS
Sequence in context: A293620 A206980 A357816 * A209219 A207688 A208495
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 31 2010
EXTENSIONS
More terms from Robin Visser, Aug 08 2023
STATUS
approved

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Last modified May 20 03:01 EDT 2024. Contains 372703 sequences. (Running on oeis4.)