cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A009017 Expansion of e.g.f. cos(x*exp(x)).

This page as a plain text file.
%I A009017 #20 Sep 08 2022 08:44:37
%S A009017 1,0,-1,-6,-23,-60,-1,1526,15121,106344,579359,1870418,-8716487,
%T A009017 -251210388,-3217413473,-31518844530,-245728084447,-1260370850736,
%U A009017 3075924210623,208464730479658,3846319817704841,52691292058337940
%N A009017 Expansion of e.g.f. cos(x*exp(x)).
%H A009017 G. C. Greubel, <a href="/A009017/b009017.txt">Table of n, a(n) for n = 0..250</a>
%F A009017 a(n) = Sum_{k=0..n/2} binomial(n,2*k)*(2*k)^(n-2*k)*(-1)^k, n>0, a(0)=1. - _Vladimir Kruchinin_, Jun 29 2011
%t A009017 With[{nmax = 50}, CoefficientList[Series[Cos[x*Exp[x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jul 21 2018 *)
%o A009017 (Maxima)
%o A009017 a(n):=if n=0 then 1 else sum(binomial(n,2*k)*(2*k)^(n-2*k)*(-1)^k,k,0,n/2); /* _Vladimir Kruchinin_, Jun 29 2011 */
%o A009017 (PARI) x='x+O('x^30); Vec(serlaplace(cos(x*exp(x)))) \\ _G. C. Greubel_, Jul 21 2018
%o A009017 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(x*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 21 2018
%K A009017 sign,easy
%O A009017 0,4
%A A009017 _R. H. Hardin_
%E A009017 Extended with signs by _Olivier Gérard_, Mar 15 1997