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Expansion of e.g.f.: cos(sinh(x)*log(1+x)).
1

%I #18 Sep 08 2022 08:44:37

%S 1,0,0,0,-12,60,-450,2940,-20720,155232,-1186920,9474960,-74648376,

%T 552593184,-3012161152,-10103577120,836086634240,-22797582691456,

%U 523741123519296,-11502212537522304,251821773466887808

%N Expansion of e.g.f.: cos(sinh(x)*log(1+x)).

%H G. C. Greubel, <a href="/A009062/b009062.txt">Table of n, a(n) for n = 0..250</a>

%p seq(coeff(series(factorial(n)*cos(sinh(x)*log(x+1)), x,n+1),x,n),n=0..25); # _Muniru A Asiru_, Jul 24 2018

%t With[{nn=20},CoefficientList[Series[Cos[Sinh[x]*Log[1+x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Sep 06 2015 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(cos(sinh(x)*log(1+x)))) \\ _G. C. Greubel_, Jul 23 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(Sinh(x)*Log(1+x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 23 2018

%K sign,easy

%O 0,5

%A _R. H. Hardin_

%E Extended with signs by _Olivier GĂ©rard_, Mar 15 1997

%E Definition clarified and prior Mathematica program replaced by _Harvey P. Dale_, Sep 06 2015