The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A145666 a(n) = numerator of polynomial of genus 1 and level n for m = 7 : A[1,n](7). 4
 0, 7, 105, 2219, 31087, 1088129, 2538991, 17772957, 248821433, 15675750559, 21946050833, 1689845914645, 11828921402977, 1076431847676451, 7535022933740305, 263725802680934699, 3692161237533130831 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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). LINKS MAPLE A145666 := proc(n) add( 7^(n-d)/d, d=1..n-1) ; numer(%) ; end proc: seq(A145666(n), n=1..20) ; # R. J. Mathar, Feb 01 2011 MATHEMATICA 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 CROSSREFS Cf. A145609-A145640, A145656-A145687. Sequence in context: A067420 A131869 A132867 * A238464 A096131 A049210 Adjacent sequences:  A145663 A145664 A145665 * A145667 A145668 A145669 KEYWORD frac,nonn AUTHOR Artur Jasinski, Oct 16 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 16 22:04 EDT 2021. Contains 343955 sequences. (Running on oeis4.)