A080527
Expansion of e.g.f. exp(3*cosh(x))/e^3 (even powers only).
Original entry on oeis.org
1, 3, 30, 543, 14745, 546618, 26119965, 1547467743, 110507211390, 9310580616243, 910032696123645, 101790848712790218, 12883623878563854105, 1827803943114479006043, 288318381606931126782270, 50215020818975432279332743, 9597691024295026236008687265
Offset: 0
exp(3*cosh(x))/exp(3) = 1 + 3*x^2/2! + 30*x^4/4! + ...
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With[{nn=30},Take[CoefficientList[Series[Exp[3Cosh[x]]/E^3,{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* Harvey P. Dale, Dec 15 2013 *)
A081566
Second binomial transform of expansion of exp(3cosh(x)).
Original entry on oeis.org
1, 2, 7, 26, 118, 572, 3127, 18146, 114793, 765602, 5463982, 40870436, 323326813, 2667777842, 23092966267, 207651618746, 1947316349278, 18906249136892, 190564801592107, 1982986181092226, 21345005629846213, 236628248493001202
Offset: 0
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m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(3*Cosh(x)+2*x-3) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 13 2019
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seq(coeff(series(exp(3*cosh(x)+2*x-3), x, n+1)*factorial(n), x, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019
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With[{nn = 30}, CoefficientList[Series[Exp[3 Cosh[x] + 2 x - 3], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Aug 08 2013 *)
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my(x='x+O('x^30)); Vec(serlaplace( exp(3*cosh(x)+2*x-3) )) \\ G. C. Greubel, Aug 13 2019
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[factorial(n)*( exp(3*cosh(x)+2*x-3) ).series(x,n+1).list()[n] for n in (0..30)] # G. C. Greubel, Aug 13 2019
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