A012308 - OEIS

%I #11 Sep 08 2022 08:44:38

%S 1,0,0,0,-12,60,-450,2940,-23408,179424,-1610280,13910160,-137455032,

%T 1245692448,-12516311808,93103526880,-527152105728,-11362927602816,

%U 427180646000448,-13403925787199616,328077695114329728

%N Expansion of e.g.f. cos(arcsin(x)*log(x+1))=1-12/4!*x^4+60/5!*x^5-450/6!*x^6+2940/7!*x^7...

%H G. C. Greubel, <a href="/A012308/b012308.txt">Table of n, a(n) for n = 0..449</a>

%e E.g.f. = 1 - 12*x^4/4! + 60*x^5/5! - 450*x^6/6! + 2940*x^7/7! + ...

%p seq(coeff(series(factorial(n)*cos(arcsin(x)*log(x+1)),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Oct 25 2018

%t With[{nn = 30}, CoefficientList[Series[Cos[ArcSin[x] Log[x + 1]], {x, 0, nn}], x] Range[0, nn]!] (* _G. C. Greubel_, Oct 25 2018 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(cos(asin(x)*log(x+1)))) \\ _G. C. Greubel_, Oct 25 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Cos(Arcsin(x)*Log(x+1)) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // _G. C. Greubel_, Oct 25 2018

%K sign

%O 0,5

%A Patrick Demichel (patrick.demichel(AT)hp.com)