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A009132
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Expansion of e.g.f. cosh(log(1+x))/exp(x).
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2
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1, -1, 2, -7, 31, -161, 976, -6847, 54797, -493201, 4932046, -54252551, 651030667, -8463398737, 118487582396, -1777313736031, 28437019776601, -483429336202337, 8701728051642202, -165332832981201991, 3306656659624039991
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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.: (2+2*x+x^2)/(2*(1+x)*exp(x)) =(1+x/(G(0))/2 ; G(k) = 1 - 1/(1 + x + x^2 - (x*(1+x))^2/(x*(1+x) - (k+1)/(1 + x/G(k+1)))) ; (continued fraction). - Sergei N. Gladkovskii, Dec 28 2011
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MATHEMATICA
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With[{nmax = 30}, CoefficientList[Series[Cosh[Log[1 + x]]/Exp[x], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jul 28 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+x))/exp(x))) \\ G. C. Greubel, Jul 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+x))/Exp(x))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 28 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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