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A009123
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Expansion of e.g.f.: cosh(log(1+sin(x))).
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3
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1, 0, 1, -3, 8, -30, 136, -693, 3968, -25260, 176896, -1351383, 11184128, -99680490, 951878656, -9695756073, 104932671488, -1202439837720, 14544442556416, -185185594118763, 2475749026562048, -34674437196568950
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OFFSET
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0,4
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COMMENTS
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|a(n)| = number of even alternating permutations on n letters (offset 1). - Vladeta Jovovic, May 20 2007
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LINKS
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FORMULA
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G.f.: (1+x/(1+x^2))/2 + 1/2/Q(0) where Q(k) = 1 + (k+1)*x - x^2*(k+1)*(k+2)/2 /Q(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Mar 12 2013
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MATHEMATICA
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CoefficientList[Series[(1 + (1 + Sin[x])^2)/(2*(1 + Sin[x])), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 22 2015 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+sin(x))))) \\ G. C. Greubel, Jul 26 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+Sin(x))))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 26 2018
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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