1,2

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]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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

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;

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]

Equals 2 * A000698(n+1), n>0.

Sequence in context: A078253 A006442 A084212 this_sequence A112698 A025168 A084358

Adjacent sequences: A004205 A004206 A004207 this_sequence A004209 A004210 A004211

nonn

N. J. A. Sloane (njas(AT)research.att.com).

Description corrected by Jeremy Magland (magland(AT)math.byu.edu), Jan 07 2000

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 21 2003