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A145666
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a(n) = numerator of polynomial of genus 1 and level n for m = 7 : A[1,n](7).
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4
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0, 7, 105, 2219, 31087, 1088129, 2538991, 17772957, 248821433, 15675750559, 21946050833, 1689845914645, 11828921402977, 1076431847676451, 7535022933740305, 263725802680934699, 3692161237533130831
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OFFSET
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1,2
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COMMENTS
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For numerator of polynomial of genus 1 and level n for m = 1 see A001008.
Definition: The polynomial A[1,n](m) = A[genus 1,level n] is here defined as
Sum_{d=1..n-1} m^(n - d)/d
Few first A[1,n](m):
n=1: A[1,1](m)= 0;
n=2: A[1,2](m)= m;
n=3: A[1,3](m)= m/2 + m^2;
n=4: A[1,4](m)= m/3 + m^2/2 + m^3;
n=5: A[1,5](m)= m/4 + m^2/3 + m^3/2 + m^4.
General formula which uses these polynomials is:
(1/(n+1))Hypergeometric2F1[1,n,n+1,1/m] =
Sum_{x>=0} m^(-x)/(x+n) =
m^(n)*arctanh((2m-1)/(2m^2-2m+1)) - A[1,n](m) =
m^(n)*log(m/(m-1)) - A[1,n](m).
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LINKS
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MAPLE
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A145666 := proc(n) add( 7^(n-d)/d, d=1..n-1) ; numer(%) ; end proc:
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MATHEMATICA
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m = 7; aa = {}; Do[k = 0; Do[k = k + m^(r - d)/d, {d, 1, r - 1}]; AppendTo[aa, Numerator[k]], {r, 1, 30}]; aa
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CROSSREFS
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KEYWORD
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frac,nonn
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AUTHOR
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STATUS
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approved
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