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 A013170 Expansion of e.g.f.: exp(arctanh(x)+arcsin(x)). 2

%I #21 May 10 2020 02:59:35

%S 1,2,4,11,40,185,1030,6785,51160,438425,4176250,44098925,507867100,

%T 6375156125,86130937750,1253044612625,19429666282000,321457635604625,

%U 5626346310003250,104323833636303125,2034312191276462500

%N Expansion of e.g.f.: exp(arctanh(x)+arcsin(x)).

%H Vincenzo Librandi, <a href="/A013170/b013170.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = n * A006228(n) + A006228(n+1). - _Mark van Hoeij_, Aug 27 2005

%F a(n) = (n^2-3*n+5)*a(n-2) + (n^2-6*n+10)*a(n-3). - _Vaclav Kotesovec_, Oct 07 2012

%e exp(arctanh(x)+arcsin(x)) = 1+2*x+4/2!*x^2+11/3!*x^3+40/4!*x^4+185/5!*x^5+...

%t Table[n!*SeriesCoefficient[E^(ArcTanh[x]+ArcSin[x]),{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 07 2012 *)

%o (PARI) x='x+O('x^66); Vec(serlaplace(exp(atanh(x)+asin(x)))) \\ _Joerg Arndt_, May 04 2013

%Y Cf. A006228.

%K nonn

%O 0,2

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

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Last modified December 11 02:45 EST 2023. Contains 367717 sequences. (Running on oeis4.)