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 A003702 Expansion of tan(x)/cosh(x). (Formerly M5110) 5

%I M5110 #24 Oct 29 2023 01:42:32

%S 1,-1,21,-141,10441,-183481,29429661,-987318021,276117553681,

%T -15085947275761,6514632269358501,-526614587249608701,

%U 324871912636292700121,-36433570919762397948841,30417659816002454665514541

%N Expansion of tan(x)/cosh(x).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vaclav Kotesovec, <a href="/A003702/b003702.txt">Table of n, a(n) for n = 0..240</a> (first 50 terms from T. D. Noe)

%F a(n) ~ (2*exp(Pi/2) + (exp(Pi) - 1)*(-1)^n) * (2*n+1)! * 2^(2*n+3) / ((1+exp(Pi)) * Pi^(2*n+2)). - _Vaclav Kotesovec_, Feb 16 2015

%t Tan[ x ]/Cosh[ x ] (* Odd Part *)

%t nn = 20; Table[(CoefficientList[Series[Sech[x]*Tan[x], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Feb 16 2015 *)

%K sign

%O 0,3

%A _R. H. Hardin_, _Simon Plouffe_

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Last modified February 23 22:58 EST 2024. Contains 370288 sequences. (Running on oeis4.)