Search: id:A145609
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%I A145609
%S A145609 3,25,49,761,7381,86021,1171733,2436559,14274301,55835135,19093197,
%T A145609 1347822955,34395742267,315404588903,9304682830147,586061125622639,
%U A145609 54062195834749,54801925434709,2053580969474233,2078178381193813
%N A145609 Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index 
               l=2n+1 evaluated at x=1.
%C A145609 For denominators see A145610.
%C A145609 The polynomials A_{2n+1}(x) = sum_{d=1..2n} x^(2n+1-d)/d for small n 
               look as follows:
%C A145609 n=1, index = 3: A_3(x) = x/2 + x^2.
%C A145609 n=2, index = 5: A_5(x) = x/4 + x^2/3 + x^3/2 + x^4.
%C A145609 n=3, index = 7: A_7(x) = x/6 + x^2/5 + x^3/4 + x^4/3 + x^5/2 + x^6.
%C A145609 n=4, index = 9: A_9(x) = x/8 + x^2/7 + x^3/6 + x^4/5 + x^5/4 + x^6/3 
               + x^7/2 + x^8.
%F A145609 (1/(2n+1))*2F1(1,2n+1;2n+2;1/m) = Sum_{x=0..infinity} m^(-x)/(x+2n+1) 
               =
%F A145609 m^(2n)arctanh((2m-1)/(2m^2-2m+1))-A_{2n+1}(m) = m^(2n)log(m/(m-1))-A_{2n+1}(m) 
               [Artur Jasinski, Oct 14 2008]
%p A145609 A := proc(l,x) add(x^(l-d)/d,d=1..l-1) ; end: A145609 := proc(n) numer( 
               A(2*n+1,1)) ; end: seq(A145609(n),n=1..20) ; # R. J. Mathar, Aug 
               21 2009
%t A145609 m = 1; 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*)
%Y A145609 Cf. A145609 - A145640.
%Y A145609 Sequence in context: A129599 A042899 A051280 this_sequence A120285 A041897 
               A006222
%Y A145609 Adjacent sequences: A145606 A145607 A145608 this_sequence A145610 A145611 
               A145612
%K A145609 frac,nonn
%O A145609 1,1
%A A145609 Artur Jasinski (grafix(AT)csl.pl), Oct 14 2008
%E A145609 Edited, parentheses in front of Gauss. Hypg. Fct. added by R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Aug 21 2009

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