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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

Table of n, a(n) for n=1..17.

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

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Last modified August 22 20:47 EDT 2019. Contains 326209 sequences. (Running on oeis4.)