A085471 Triangle of coefficients of numerators of powers of e^2 in Sum_{k>=1} {1 / (1 + (k+1/2)^2*Pi^2)^n} + {4^n / (4+Pi^2)^n}.

1, -1, 1, -4, -1, 3, -17, -7, -3, 15, -94, -56, -58, -15, 105, -657, -578, -982, -503, -105, 945, -5584, -7291, -16824, -12901, -5464, -945, 10395, -55757, -106209, -303361, -313199, -202071, -70411, -10395, 135135, -634722, -1728758, -5846866, -7692464, -6715286, -3535066

Offset

1,4

Links

Table of n, a(n) for n=1..42.

Eric Weisstein's World of Mathematics, Infinite Series

Example

{-1 + e^2, -1 - 4*e^2 + e^4, -3 - 7*e^2 - 17*e^4 + 3*e^6}

Mathematica

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) ]

Crossrefs

Sequence in context: A336693 A193793 A301510 * A064221 A229672 A298568

Adjacent sequences: A085468 A085469 A085470 * A085472 A085473 A085474

Keyword

sign,tabl

Author

Eric W. Weisstein, Jul 01 2003

Status

approved