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A341873
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Coefficients of the series whose 24th power equals E_2(x)^5/E_10(x), where E_2(x) and E_10(x) are the Eisenstein series A006352 and A013974.
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1
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1, 6, 7038, 2002644, 922569342, 380737463400, 175255606306116, 80315525064955440, 38028486993289854966, 18171889608389845598586, 8807723964899085718419480, 4305311468773791666900669828, 2122088430918938935321961736084
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OFFSET
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0,2
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COMMENTS
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It is easy to see that E_2(x)^5/E_10(x) == 1 - 24*Sum_{k >= 1} (5*k - 11*k^9)*x^k/(1 - x^k) (mod 144), and also that the integer 5*k - 11*k^9 is always divisible by 6. Hence, E_2(x)^5/E_10(x) == 1 (mod 144). It follows from Heninger et al., p. 3, Corollary 2, that the series expansion of (E_2(x)^5/E_10(x))^(1/24) = 1 + 6*x + 7038*x^2 + 2002644*x^3 + 922569342*x^4 + ... has integer coefficients.
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LINKS
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MAPLE
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E(2, x) := 1 - 24*add(k*x^k/(1-x^k), k = 1..20):
E(10, x) := 1 - 264*add(k^9*x^k/(1-x^k), k = 1..20):
with(gfun): series((E(2, x)^5/E(10, x))^(1/24), x, 20):
seriestolist(%);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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