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%I #6 Mar 27 2019 03:53:00
%S 1,-1,1,1,-11,43,-83,-275,3833,-21561,51369,375593,-5860147,40452371,
%T -101676235,-1409619211,23912208945,-189650997937,454996127889,
%U 11250036170129,-204691511497499,1799897065507003,-3741969787709699,-164548323889940675,3183842522596250537,-30356999697044585833
%N Expansion of e.g.f. exp(cos(x)/exp(x) - 1).
%e exp(cos(x)/exp(x) - 1) = 1 - x + x^2/2! + x^3/3! - 11*x^4/4! + 43*x^5/5! - 83*x^6/6! - 275*x^7/7! + ...
%p a:=series(exp(cos(x)/exp(x)-1),x=0,26): seq(n!*coeff(a,x,n),n=0..25); # _Paolo P. Lava_, Mar 26 2019
%t nmax = 25; CoefficientList[Series[Exp[Cos[x]/Exp[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
%t a[n_] := a[n] = Sum[Re[(-1 - I)^k] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 25}]
%Y Cf. A004211, A009116, A009216, A009235, A009255, A009276, A146559, A155585.
%K sign
%O 0,5
%A _Ilya Gutkovskiy_, Jun 08 2018
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