%I A085471
%S A085471 1,1,1,4,1,3,17,7,3,15,94,56,58,15,105,657,578,982,503,105,945,5584,
%T A085471 7291,16824,12901,5464,945,10395,55757,106209,303361,313199,202071,
%U A085471 70411,10395,135135,634722,1728758,5846866,7692464,6715286,3535066
%V A085471 1,-1,1,-4,-1,3,-17,-7,-3,15,-94,-56,-58,-15,105,-657,-578,-982,-503,-105,
               945,-5584,
%W A085471 -7291,-16824,-12901,-5464,-945,10395,-55757,-106209,-303361,-313199,-202071,
               -70411,
%X A085471 -10395,135135,-634722,-1728758,-5846866,-7692464,-6715286,-3535066
%N A085471 Triangle of coefficients of numerators of powers of e^2 in sum_{k=1..infty} 
               {1 / [1+(k+1/2)^2*pi^2]^n}+{4^n / (4+pi^2)^n}.
%H A085471 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               InfiniteSeries.html">Infinite Series</a>
%e A085471 {-1 + e^2, -1 - 4*e^2 + e^4, -3 - 7*e^2 - 17*e^4 + 3*e^6}
%t A085471 q = FullSimplify[ TrigToExp[ Table[ (Sum[ 1/(1 + (k + 1/2)^2*Pi^2)^n, 
               {k, Infinity} ] + 4^n/(4 + Pi^2)^n)*(n - 1)!*2^n*(E^2 + 1)^n, {n, 
               8} ] ] ]; Flatten[ Reverse/@(CoefficientList[ #, E^2 ]&/@q) ]
%Y A085471 Sequence in context: A093735 A156224 A162516 this_sequence A064221 A152890 
               A143354
%Y A085471 Adjacent sequences: A085468 A085469 A085470 this_sequence A085472 A085473 
               A085474
%K A085471 sign,tabl
%O A085471 1,4
%A A085471 Eric Weisstein (eric(AT)weisstein.com), Jul 01, 2003