A013076 - OEIS

%I #13 Jul 01 2021 16:17:57

%S 0,2,-1,-15,42,405,-2970,-20475,335160,1357965,-54999000,-31340925,

%T 12203314200,-48569546025,-3449672226000,35421501740625,

%U 1174230285228000,-23134846868508375,-448847662070808000

%N Expansion of e.g.f. tanh(arcsinh(x) + log(x+1)).

%H Muniru A Asiru, <a href="/A013076/b013076.txt">Table of n, a(n) for n = 0..100</a>

%e 2*x - 1/2!*x^2 - 15/3!*x^3 + 42/4!*x^4 + 405/5!*x^5 ...

%p seq(coeff(series(factorial(n)*tanh(arcsinh(x)+log(x+1)), x,n+1),x,n),n=0..20); # _Muniru A Asiru_, Jul 30 2018

%t With[{nn=20},CoefficientList[Series[Tanh[ArcSinh[x]+Log[x+1]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 01 2021 *)

%o (PARI) x = 'x + O('x^30); concat([0], Vec(serlaplace(tanh(asinh(x) + log(x+1))))) \\ _Michel Marcus_, Jul 30 2018

%K sign

%O 0,2

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

%E a(0)=0 inserted and title improved by _Sean A. Irvine_, Jul 30 2018