A012313 - OEIS

%I #13 Sep 08 2022 08:44:38

%S 1,0,0,0,12,-60,450,-2940,26768,-239904,2668680,-29987760,392312712,

%T -5250012768,78929218368,-1221015912480,20751350980608,

%U -363744987018624,6898607729825472,-135014880247703424

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

%H G. C. Greubel, <a href="/A012313/b012313.txt">Table of n, a(n) for n = 0..448</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)*cosh(arcsin(x)*log(x+1)),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Oct 25 2018

%t With[{nn=20},CoefficientList[Series[Cosh[ArcSin[x]Log[x+1]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Aug 02 2017 *)

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

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Cosh(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)

%E Definition clarified by _Harvey P. Dale_, Aug 02 2017