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A004208
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a(n) = n(2n-1)!!- Sum a(k)(2n-2k-1)!!.
(Formerly M3985)
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3
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1, 5, 37, 353, 4081, 55205, 854197, 14876033, 288018721, 6138913925, 142882295557, 3606682364513, 98158402127761, 2865624738913445, 89338394736560917, 2962542872271918593, 104128401379446177601
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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]
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| 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
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MAPLE
| 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;
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MATHEMATICA
| 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]
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CROSSREFS
| Equals 2 * A000698(n+1), n>0.
Sequence in context: A199562 A177395 A197713 * A198077 A112698 A025168
Adjacent sequences: A004205 A004206 A004207 * A004209 A004210 A004211
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| 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
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