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.

A009024 Expansion of e.g.f.: x*cos(log(1+x)).

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%I A009024 #22 Sep 08 2022 08:44:37
%S A009024 0,1,0,-3,12,-50,240,-1330,8400,-59580,468000,-4018300,37237200,
%T A009024 -367507400,3802780800,-40373385000,423927504000,-4048235126000,
%U A009024 25093796832000,288695417426000,-18721925937000000,623644389813900000
%N A009024 Expansion of e.g.f.: x*cos(log(1+x)).
%H A009024 G. C. Greubel, <a href="/A009024/b009024.txt">Table of n, a(n) for n = 0..250</a>
%F A009024 a(n) = n * A003703(n-1).
%F A009024 a(n+3) = -a(n+2)*(2*n+1)*(n+3)/(n+2) - a(n+1)*(1+n^2)*(n+3)/(n+1), a(0)=0, a(1)=1, a(2)=0. - _Sergei N. Gladkovskii_, Aug 17 2012
%t A009024 With[{nmax = 30}, CoefficientList[Series[x*Cos[Log[1 + x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jul 22 2018 *)
%o A009024 (PARI) x='x+O('x^30); concat([0], Vec(serlaplace(x*cos(log(1+x))))) \\ _G. C. Greubel_, Jul 22 2018
%o A009024 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:= [0] cat Coefficients(R!(x*Cos(Log(1+x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 22 2018
%K A009024 sign,easy
%O A009024 0,4
%A A009024 _R. H. Hardin_
%E A009024 Extended with signs by _Olivier Gérard_, Mar 15 1997