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Search: id:A085471
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| A085471 |
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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}. |
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+0
1
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| 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
(list; table; graph; listen)
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OFFSET
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1,4
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LINKS
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Eric Weisstein's World of Mathematics, Infinite Series
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EXAMPLE
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{-1 + e^2, -1 - 4*e^2 + e^4, -3 - 7*e^2 - 17*e^4 + 3*e^6}
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MATHEMATICA
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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) ]
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CROSSREFS
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Sequence in context: A074081 A132703 A093735 this_sequence A064221 A106141 A082999
Adjacent sequences: A085468 A085469 A085470 this_sequence A085472 A085473 A085474
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KEYWORD
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sign,tabl
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Jul 01, 2003
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