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 A145619 Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=6. 1

%I #11 Jun 05 2016 23:33:35

%S 39,2835,255191,257233353,2315100338,1833559470601,429052916136639,

%T 123567239847463143,56717363089986833887,2586311756903401044465,

%U 46553611624261219442817,154185561699553158848604845

%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=6.

%C For denominators see A145620. For general properties of A_l(x) see A145609.

%t m = 6; 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_ *)

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

%t Table[6 a[2 n, 6] // FullSimplify // 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

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Last modified September 14 06:05 EDT 2024. Contains 375911 sequences. (Running on oeis4.)