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%I #14 Sep 08 2022 08:45:09
%S 1,2,7,26,118,572,3127,18146,114793,765602,5463982,40870436,323326813,
%T 2667777842,23092966267,207651618746,1947316349278,18906249136892,
%U 190564801592107,1982986181092226,21345005629846213,236628248493001202
%N Second binomial transform of expansion of exp(3cosh(x)).
%C Binomial transform of A081565.
%H Vincenzo Librandi, <a href="/A081566/b081566.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: exp(2*x) * exp(3*cosh(x))/e^3 = exp(3*cosh(x)+2*x-3).
%p 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
%t With[{nn = 30}, CoefficientList[Series[Exp[3 Cosh[x] + 2 x - 3], {x, 0, nn}], x] Range[0, nn]!] (* _Vincenzo Librandi_, Aug 08 2013 *)
%o (PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(3*cosh(x)+2*x-3) )) \\ _G. C. Greubel_, Aug 13 2019
%o (Magma) m:=30; R<x>:=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
%o (Sage) [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
%Y Cf. A081564, A081565.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Mar 22 2003
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