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A170991
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Number of genus 2, degree n, simply ramified covers of an elliptic curve.
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8
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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
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OFFSET
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2,1
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COMMENTS
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The reference gives a generating function and the terms up to degree 18.
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LINKS
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FORMULA
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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
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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