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A081558
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Exponential generating function: exp(cosh(x)+2*x-1).
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2
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1, 2, 5, 14, 44, 152, 575, 2354, 10379, 48902, 245240, 1301984, 7294589, 42959282, 265263185, 1712168654, 11528506124, 80783015192, 588097479635, 4439382164114, 34699233959759, 280381494540182, 2339287666524440, 20125268756209664, 178348602246900569
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OFFSET
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0,2
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COMMENTS
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Old definition was "Second binomial transform of expansion of exp(cosh(x))".
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LINKS
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FORMULA
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E.g.f.: exp(2*x) * exp(cosh(x))/e.
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MAPLE
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seq(coeff(series(exp(cosh(x)+2*x-1), x, n+1)*factorial(n), x, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019
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MATHEMATICA
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With[{nn = 30}, CoefficientList[Series[Exp[Cosh[x] + 2 x - 1], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Aug 08 2013 *)
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PROG
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(PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(cosh(x)+2*x-1) )) \\ G. C. Greubel, Aug 13 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Cosh(x)+2*x-1) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 13 2019
(Sage) [factorial(n)*( exp(cosh(x)+2*x-1) ).series(x, n+1).list()[n] for n in (0..30)] # G. C. Greubel, Aug 13 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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