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A145666 a(n) = numerator of polynomial of genus 1 and level n for m = 7 : A[1,n](7).

%I A145666 #10 Jan 20 2019 23:20:22
%S A145666 0,7,105,2219,31087,1088129,2538991,17772957,248821433,15675750559,
%T A145666 21946050833,1689845914645,11828921402977,1076431847676451,
%U A145666 7535022933740305,263725802680934699,3692161237533130831
%N A145666 a(n) = numerator of polynomial of genus 1 and level n for m = 7 : A[1,n](7).
%C A145666 For numerator of polynomial of genus 1 and level n for m = 1 see A001008.
%C A145666 Definition: The polynomial A[1,n](m) = A[genus 1,level n] is here defined as
%C A145666 Sum_{d=1..n-1} m^(n - d)/d
%C A145666 Few first A[1,n](m):
%C A145666 n=1: A[1,1](m)= 0;
%C A145666 n=2: A[1,2](m)= m;
%C A145666 n=3: A[1,3](m)= m/2 + m^2;
%C A145666 n=4: A[1,4](m)= m/3 + m^2/2 + m^3;
%C A145666 n=5: A[1,5](m)= m/4 + m^2/3 + m^3/2 + m^4.
%C A145666 General formula which uses these polynomials is:
%C A145666 (1/(n+1))Hypergeometric2F1[1,n,n+1,1/m] =
%C A145666 Sum_{x>=0} m^(-x)/(x+n) =
%C A145666 m^(n)*arctanh((2m-1)/(2m^2-2m+1)) - A[1,n](m) =
%C A145666 m^(n)*log(m/(m-1)) - A[1,n](m).
%p A145666 A145666 := proc(n) add( 7^(n-d)/d,d=1..n-1) ; numer(%) ; end proc:
%p A145666 seq(A145666(n),n=1..20) ; # _R. J. Mathar_, Feb 01 2011
%t A145666 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
%Y A145666 Cf. A145609-A145640, A145656-A145687.
%K A145666 frac,nonn
%O A145666 1,2
%A A145666 _Artur Jasinski_, Oct 16 2008