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%I #17 Sep 08 2022 08:44:37
%S 1,0,0,-3,11,-30,194,-1785,13957,-113148,1143284,-13131855,156950639,
%T -2005222362,28119703702,-424785970245,6792043718345,-115135087505400,
%U 2072993596779944,-39432571052652315,788564865102950035
%N Expansion of e.g.f. cosh(log(1+x))/cosh(x).
%H G. C. Greubel, <a href="/A009131/b009131.txt">Table of n, a(n) for n = 0..250</a>
%F a(n) ~ n! * (-1)^n / (exp(1) + exp(-1)). - _Vaclav Kotesovec_, Jan 22 2015
%t CoefficientList[Series[((1 + (1 + x)^2)*Sech[x])/(2*(1 + x)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 22 2015 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+x))/cosh(x))) \\ _G. C. Greubel_, Jul 28 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+x))/Cosh(x))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 28 2018
%K sign,easy
%O 0,4
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997