%I A105639
%S A105639 0,1,3,51,2635,321315,79244571,35534634163,26790753983211,31980883597248195,
%T A105639 57639013468037578555,150903079070698932214611,555841597474333410204232203,
%U A105639 2804056152239296833617706906211,18933384891214439885244043983467355
%N A105639 Multiples of coefficients in an asymptotic series of Ramanujan.
%D A105639 G. H. Hardy, Srinivasa Ramanujan (1887-1920), pp. xxi-xxxvi of Collected 
               Papers of Srinivasa Ramanujan, Ed. G. H. Hardy et al., AMS Chelsea 
               2000. See page xxvi VII. (4)
%F A105639 a(n)=-G(n)G(n+1) where G=A001469 Genocchi numbers.
%F A105639 Sum_{k>0} k^2/(e^(kx)-1) = zeta(3)2/x^3 -1/(12x) + Sum_{k>0} a(k)x^(2k-1)/
               ((2k)!(2k+2)4(2^(2k)-1)(2^(2k+2)-1)).
%e A105639 x/1440 +x^3/181440 +x^5/7257600 +x^7/159667200 +691x^9/1569209241600 
               +...
%o A105639 (PARI) a(n)=if(n<0,0, n*=2; -4*(2^n-1)*(4*2^n-1)*bernfrac(n)*bernfrac(n+2))
%Y A105639 Cf. A001469.
%Y A105639 Sequence in context: A145242 A075869 A126685 this_sequence A003028 A069343 
               A084882
%Y A105639 Adjacent sequences: A105636 A105637 A105638 this_sequence A105640 A105641 
               A105642
%K A105639 nonn
%O A105639 0,3
%A A105639 Michael Somos, Apr 16 2005