A012513 - OEIS

%I #11 Jul 04 2021 20:03:22

%S 0,0,2,-3,12,-40,-50,1449,-23016,261288,-2306342,15798365,33379940,

%T -3972201168,100308059878,-1917671123655,28943854480688,

%U -288514829730256,-1435208344849998,189049167829499229

%N Expansion of e.g.f. arctan(sinh(x) * log(x+1)).

%H Muniru A Asiru, <a href="/A012513/b012513.txt">Table of n, a(n) for n = 0..100</a>

%e 2/2!*x^2 - 3/3!*x^3 + 12/4!*x^4 - 40/5!*x^5 ...

%p seq(coeff(series(factorial(n)*arctan(sinh(x)*log(x+1)), x,n+1),x,n),n=0..20); # _Muniru A Asiru_, Jul 19 2018

%t With[{nn=20},CoefficientList[Series[ArcTan[Sinh[x]Log[x+1]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 04 2021 *)

%K sign

%O 0,3

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

%E a(0) and a(1) inserted and title improved by _Sean A. Irvine_, Jul 19 2018