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A013559
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Numerator of [x^n] in the Taylor expansion of exp(cosech(x)-coth(x)).
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1
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1, -1, 1, 1, -7, 1, 97, -55, -2063, 143, 17803, -968167, -250781, 7000033, -166831871, -571772647, 43685848289, 843598411471, -447550424579, -1263845119891, 84677077231169, 740683182137153, -11657476758734011, -474904166544135457, 28924058075775365981, -2379183287545454197
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OFFSET
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0,5
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COMMENTS
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The inner function is cosech(x)-coth(x) = -x/2 +x^3/24 -x^5/240 +17*x^7/40320 -31*x^9/725760 +691*x^11/159667200 -... with e.g.f numerators cosech(x)-coth(x) = sum b(n)x^n/(n+1)! apparently in A001469.
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LINKS
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EXAMPLE
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1-x/2 +x^2/8 +x^3/48 -7*x^4/384 +x^5/1280 +97*x^6/46080 -...
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MAPLE
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S:= series(exp(csch(x)-coth(x)), x, 51):
seq(numer(coeff(S, x, j)), j=0..50); # Robert Israel, Nov 14 2016
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MATHEMATICA
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Numerator[Take[CoefficientList[Series[Exp[Csch[x] - Coth[x]], {x, 0, 40}], x], {1, -1, 1}]] (* G. C. Greubel, Nov 13 2016 *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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Patrick Demichel (patrick.demichel(AT)hp.com)
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EXTENSIONS
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STATUS
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approved
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