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A081562
Binomial transform of expansion of exp(2cosh(x)), A000807.
3
1, 1, 3, 7, 27, 91, 423, 1807, 9747, 49651, 303183, 1777447, 12072987, 79587691, 593485623, 4327497727, 35069154147, 279393234211, 2440577314143, 21043100301847, 196825339400427, 1822706292362011, 18153886768953543
OFFSET
0,3
LINKS
FORMULA
E.g.f.: exp(x)+exp(2*cosh(x))/e^2 = exp(2*cosh(x)+x-2).
MAPLE
seq(coeff(series(exp(2*cosh(x)+x-2), x, n+1)*factorial(n), x, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019
MATHEMATICA
With[{nn = 30}, CoefficientList[Series[Exp[2 Cosh[x] + x - 2], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Aug 08 2013 *)
PROG
(PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(2*cosh(x)+x-2) )) \\ G. C. Greubel, Aug 13 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(2*Cosh(x)+x-2) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 13 2019
(Sage) [factorial(n)*( exp(2*cosh(x)+x-2) ).series(x, n+1).list()[n] for n in (0..30)] # G. C. Greubel, Aug 13 2019
CROSSREFS
Sequence in context: A148749 A098465 A148750 * A216174 A260464 A346658
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 22 2003
STATUS
approved