cp's OEIS Frontend

A145664 a(n) = numerator of polynomial of genus 1 and level n for m = 6 = A[1,n](6).

%I A145664 #12 Jan 21 2019 04:18:57
%S A145664 0,6,39,236,2835,42531,255191,10718052,257233353,2315100317,
%T A145664 2315100338,152796622518,1833559470601,71508819355749,429052916136639,
%U A145664 2574317496821836,123567239847463143,6301929232220740413
%N A145664 a(n) = numerator of polynomial of genus 1 and level n for m = 6 = A[1,n](6).
%C A145664 For numerator of polynomial of genus 1 and level n for m = 1 see A001008.
%C A145664 Definition: The polynomial A[1,2n+1](m) = A[genus 1,level n] is here defined as
%C A145664 Sum_{d=1..n-1} m^(n-d)/d.
%C A145664 Few first A[1,n](m):
%C A145664 n=1: A[1,1](m)= 0;
%C A145664 n=2: A[1,2](m)= m;
%C A145664 n=3: A[1,3](m)= m/2 + m^2;
%C A145664 n=4: A[1,4](m)= m/4 + m^2/3 + m^3/2 + m^4;
%C A145664 General formula which uses these polynomials is:
%C A145664 (1/(n+1))Hypergeometric2F1[1,n,n+1,1/m] =
%C A145664 Sum_{x>=0} m^(-x)/(x+n) =
%C A145664 m^n*arctanh((2m-1)/(2m^2-2m+1)) - A[1,n](m) =
%C A145664 m^n*log(m/(m-1)) - A[1,n](m).
%p A145664 A145664 := proc(n) add( 6^(n-d)/d,d=1..n-1) ; numer(%) ; end proc:
%p A145664 seq(A145664(n),n=1..20) ; # _R. J. Mathar_, Feb 01 2011
%t A145664 m = 6; aa = {}; Do[k = 0; Do[k = k + m^(r - d)/d, {d, 1, r - 1}]; AppendTo[aa, Numerator[k]], {r, 1, 30}]; aa
%Y A145664 Cf. A145609-A145640, A145656, A145658, A145660, A145662, A145664.
%K A145664 frac,nonn
%O A145664 1,2
%A A145664 _Artur Jasinski_, Oct 16 2008