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If working in SR is good enough for your problem :

tan(x).maxima_methods().powerseries(x,0)
sum((2^(2*i1) - 1)*2^(2*i1)*(-1)^(i1 - 1)*x^(2*i1 - 1)*bern(2*i1)/factorial(2*i1), i1, 0, +Infinity)

HTH,

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