A009133 - OEIS

%I #17 Sep 08 2022 08:44:37

%S 1,0,1,-3,0,0,90,-420,3192,-36792,344640,-3424080,40458792,-515760960,

%T 6995451736,-102430659240,1603858275328,-26656736919808,

%U 469564051796928,-8742335523613056,171465068564306560,-3533692765499863680

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

%H G. C. Greubel, <a href="/A009133/b009133.txt">Table of n, a(n) for n = 0..250</a>

%F a(n) ~ (-1)^n * n! / (2 * Gamma(cos(1)) * n^(1 - cos(1))). - _Vaclav Kotesovec_, Jul 28 2018

%t With[{nmax = 30}, CoefficientList[Series[Cosh[Log[1 + x]*Cos[x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jul 28 2018 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+x)*cos(x)))) \\ _G. C. Greubel_, Jul 28 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+x)*Cos(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 28 2018

%K sign,easy

%O 0,4

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997