Search: id:A146752
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%I A146752
%S A146752 1,7,71,1159,5197,148025,730141,29616293,125438657,1319937329,
%T A146752 77390680651,76972298827,319946679037,3504590799071,289784158718029,
%U A146752 25703039917515461,1114069690728835,112203290640603311
%N A146752 a(n)=numerator of k_n such that Integrate[(1+x^(3n))/Sqrt[1-x^3],{x,0,
               1}]= k_n*(Gamma[1/3]^3)/(2^(1/3)Sqrt[3]Pi) where n=0,1,2,...
%C A146752 General formula (*Artur Jasinski*): Integrate[(1+x^(3n))/Sqrt[1-x^3],
               {x,0,1}] = G_3 * k_n =
%C A146752 G_3*A146751(n)/A146752(n) = A118292*A146751(n)/A146752(n
%C A146752 where G_3 = (Gamma[1/3]^3)/(2^(1/3)Sqrt[3]Pi)
%C A146752 For constant G_3 see A118292
%C A146752 For denominators of k_n see A146752
%F A146752 a(n)=Numerator[(1/2) (1 + Product[(2 (1 + 3 k))/(5 + 6 k), {k, 0, n - 
               1}]
%t A146752 Table[Numerator[(1/2) (1 + Product[(2 (1 + 3 k))/(5 + 6 k), {k, 0, n 
               - 1}])], {n, 0, 30}] (*Artur Jasinski*)
%Y A146752 A146753, A118292
%Y A146752 Sequence in context: A067307 A052390 A002119 this_sequence A022518 A113053 
               A022503
%Y A146752 Adjacent sequences: A146749 A146750 A146751 this_sequence A146753 A146754 
               A146755
%K A146752 nonn
%O A146752 0,2
%A A146752 Artur Jasinski (grafix(AT)csl.pl), Nov 01 2008

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