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Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=12.
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%I #9 Jun 05 2016 23:34:32

%S 150,21651,15588874,31427171529,452551270138,716841211899677,

%T 1341926748676207290,3864749036187477202407,7095679230440208145951582,

%U 6471259458161469829121064993,931861361975251655393445326142

%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=12.

%C For denominators see A145632. For general properties of A_l(x) see A145609.

%t m = 12; 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_]:=m^n(Log[m/(m-1)]-Beta[1/m,1+n,0])

%t Table[12 a[2 n, 12] // FullSimplify // Numerator,{n,1,10}] (* _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