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A145660 a(n) = numerator of polynomial of genus 1 and level n for m = 4 = A[1,n](4).

%I A145660 #13 Jan 21 2019 04:18:40
%S A145660 0,4,18,220,883,17672,23566,659868,5278979,95021762,380087174,
%T A145660 16723836916,66895348819,3478558152448,13914232622662,11131386100532,
%U A145660 178102177617521,3027737019533893,4036982692723202,306810684647167556
%N A145660 a(n) = numerator of polynomial of genus 1 and level n for m = 4 = A[1,n](4).
%C A145660 For numerator of polynomial of genus 1 and level n for m = 1 see A001008.
%C A145660 Definition: The polynomial A[1,2n+1](m) = A[genus 1,level n] is here defined as
%C A145660 Sum_{d,1,n-1} m^(n-d)/d.
%C A145660 Few first A[1,n](m):
%C A145660 n=1: A[1,1](m)= 0;
%C A145660 n=2: A[1,2](m)= m;
%C A145660 n=3: A[1,3](m)= m/2 + m^2;
%C A145660 n=4: A[1,4](m)= m/4 + m^2/3 + m^3/2 + m^4.
%C A145660 General formula which uses these polynomials is following:
%C A145660 (1/(n+1))Hypergeometric2F1[1,n,n+1,1/m] =
%C A145660 Sum_{x>=0} m^(-x)/(x+n) =
%C A145660 m^n*arctanh((2m-1)/(2m^2-2m+1)) - A[1,n](m) =
%C A145660 m^n*log(m/(m-1)) - A[1,n](m).
%p A145660 A145660 := proc(n) add( 4^(n-d)/d,d=1..n-1) ; numer(%) ; end proc: # _R. J. Mathar_, Feb 01 2011
%t A145660 m = 4; aa = {}; Do[k = 0; Do[k = k + m^(r - d)/d, {d, 1, r - 1}]; AppendTo[aa, Numerator[k]], {r, 1, 30}]; aa
%Y A145660 Cf. A145609-A145640, A145656, A145668, A145662, A145664, A145666.
%K A145660 frac,nonn
%O A145660 1,2
%A A145660 _Artur Jasinski_, Oct 16 2008