Search: id:A145666
Results 1-1 of 1 results found.

%I A145666
%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 amazing polynomial of genus 1 and level n for m = 
               7 : A[1,n](7)
%C A145666 For numerator of amazing polynomial of genus 1 and level n for m = 1 
               see A001008
%C A145666 For denominators see A145667.
%C A145666 Definition: Amazing polynomial A[1,n](m) = A[genus 1,level n] is here 
               defined as
%C A145666 Sum[m^(n - d)/d,{d,1,n-1}]
%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 amazing polynomials is following (*Artur Jasinski*):
%C A145666 (1/(n+1))Hypergeometric2F1[1,n,n+1,1/m] =
%C A145666 Sum[m^(-x)(1/(x+n),{x,0,Infinity}] =
%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)
%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 (*Artur Jasinski*)
%Y A145666 A145609-A145640, A145656-A145687.
%Y A145666 Sequence in context: A067420 A131869 A132867 this_sequence A096131 A049210 
               A002486
%Y A145666 Adjacent sequences: A145663 A145664 A145665 this_sequence A145667 A145668 
               A145669
%K A145666 frac,nonn
%O A145666 1,2
%A A145666 Artur Jasinski (grafix(AT)csl.pl), Oct 16 2008

Search completed in 0.001 seconds