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A335630
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Expansion of e.g.f. Product_{k>0} (1+tan(x)^k).
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6
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1, 1, 2, 14, 64, 616, 5072, 58064, 669184, 9417856, 137019392, 2294104064, 40350383104, 778782954496, 16050760435712, 352024447115264, 8269739647565824, 204097141026881536, 5360540853755052032, 147190808628196081664, 4270498402940171321344, 129024432217526266494976
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: exp( Sum_{k>0} (-tan(x))^k/(k*(tan(x)^k-1)) ).
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MATHEMATICA
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nmax = 25; CoefficientList[Series[Product[1 + Tan[x]^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 03 2020 *)
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PROG
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(PARI) N=40; x='x+O('x^N); Vec(serlaplace(eta(tan(x)^2)/eta(tan(x))))
(PARI) N=40; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, 1+tan(x)^k)))
(PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(sum(k=1, N, (-tan(x))^k/(k*(tan(x)^k-1))))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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