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 A145660 a(n) = numerator of polynomial of genus 1 and level n for m = 4 = A[1,n](4). 4
 0, 4, 18, 220, 883, 17672, 23566, 659868, 5278979, 95021762, 380087174, 16723836916, 66895348819, 3478558152448, 13914232622662, 11131386100532, 178102177617521, 3027737019533893, 4036982692723202, 306810684647167556 (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[1,2n+1](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/4 + m^2/3 + m^3/2 + m^4. General formula which uses these polynomials is following: (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 A145660 := proc(n) add( 4^(n-d)/d, d=1..n-1) ; numer(%) ; end proc: # R. J. Mathar, Feb 01 2011 MATHEMATICA 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 CROSSREFS Cf. A145609-A145640, A145656, A145668, A145662, A145664, A145666. Sequence in context: A275965 A071173 A143993 * A246531 A278565 A214168 Adjacent sequences:  A145657 A145658 A145659 * A145661 A145662 A145663 KEYWORD frac,nonn AUTHOR Artur Jasinski, Oct 16 2008 STATUS approved

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Last modified June 13 11:44 EDT 2021. Contains 344992 sequences. (Running on oeis4.)