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A009017
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Expansion of e.g.f. cos(x*exp(x)).
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8
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1, 0, -1, -6, -23, -60, -1, 1526, 15121, 106344, 579359, 1870418, -8716487, -251210388, -3217413473, -31518844530, -245728084447, -1260370850736, 3075924210623, 208464730479658, 3846319817704841, 52691292058337940
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n/2} binomial(n,2*k)*(2*k)^(n-2*k)*(-1)^k, n>0, a(0)=1. - Vladimir Kruchinin, Jun 29 2011
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MATHEMATICA
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With[{nmax = 50}, CoefficientList[Series[Cos[x*Exp[x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jul 21 2018 *)
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PROG
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(Maxima)
a(n):=if n=0 then 1 else sum(binomial(n, 2*k)*(2*k)^(n-2*k)*(-1)^k, k, 0, n/2); /* Vladimir Kruchinin, Jun 29 2011 */
(PARI) x='x+O('x^30); Vec(serlaplace(cos(x*exp(x)))) \\ G. C. Greubel, Jul 21 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(x*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 21 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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