A145611 - OEIS

A145611

Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=2.

%I #15 Jun 05 2016 23:32:48

%S 5,131,1327,148969,89422,7869871,204620705,32739453941,556571247527,

%T 42299423848079,84598851790183,31132377803126339,155661889412050564,

%U 3735885348093583561,216681350219210744683,429895798848743086730197

%N Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=2.

%C For denominators see A145612. For general properties of A_l(x) see A145609.

%p A := proc(l,x) add(x^(l-d)/d,d=1..l-1) ; end: A145611 := proc(n) numer( A(2*n+1,2)) ; end: seq(A145611(n),n=1..20) ; # _R. J. Mathar_, Aug 21 2009

%t m = 2; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; AppendTo[aa, Numerator[k]], {r, 1, 25}]; aa (* _Artur Jasinski_, Oct 14 2008 *)

%t a[n_,m_]:=Integrate[(m-x^n)/(m-x),{x,0,1}]+(m^n-m)Log[m/(m-1)]

%t Table[2 a[2 n, 2] // Simplify // Numerator, {n,1,25}] (* _Gerry Martens_ , Jun 04 2016 *)

%Y Cf. A145609 - A145640.

%K frac,nonn

%O 1,1

%A _Artur Jasinski_, Oct 14 2008

%E Edited by _R. J. Mathar_, Aug 21 2009