%I A004208 M3985
%S A004208 1,5,37,353,4081,55205,854197,14876033,288018721,6138913925,
%T A004208 142882295557,3606682364513,98158402127761,2865624738913445,
%U A004208 89338394736560917,2962542872271918593,104128401379446177601
%N A004208 a(n) = n(2n-1)!!- Sum a(k)(2n-2k-1)!!.
%C A004208 a(n+1) is the moment of order n for the probability density function 
               rho(x)=Pi^(-3/2)*sqrt(x/2)*exp(x/2)/(1-erf^2(I*sqrt(x/2))) on the 
               interval 0..infinity, with erf the error function and I=sqrt(-1). 
               [From Roland Groux (roland.groux(AT)orange.fr), Nov 10 2009]
%D A004208 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%F A004208 x+5/2*x^2+37/3*x^3+353/4*x^4+4081/5*x^5+55205/6*x^6+... = log(1+x+3*x^2+15*x^3+105*x^4+945*x^5+10395*x^6+...)\
                where [1, 1, 3, 15, 105, 945, 10395, ...] = A001147(double factorials) 
               . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 20 2006
%p A004208 df := proc(n) product(2*k-1,k=1..n) end: a[1] := 1: for n from 2 to 30 
               do a[n] := n*df(n)-sum(a[k]*df(n-k),k=1..n-1) od;
%t A004208 CoefficientList[Series[D[Log[Sum[(2n-1)!!x^n,{n,0,17}]],x],{x,0,16}],
               x] [From Wouter Meeussen (wouter.meeussen(AT)pandora.be), Mar 21 
               2009]
%Y A004208 Equals 2 * A000698(n+1), n>0.
%Y A004208 Sequence in context: A078253 A006442 A084212 this_sequence A112698 A025168 
               A084358
%Y A004208 Adjacent sequences: A004205 A004206 A004207 this_sequence A004209 A004210 
               A004211
%K A004208 nonn,new
%O A004208 1,2
%A A004208 N. J. A. Sloane (njas(AT)research.att.com).
%E A004208 Description corrected by Jeremy Magland (magland(AT)math.byu.edu), Jan 
               07 2000
%E A004208 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 21 2003