Search: id:A079484
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%I A079484
%S A079484 1,3,45,1575,99225,9823275,1404728325,273922023375,69850115960625,
%T A079484 22561587455281875,9002073394657468125,4348001449619557104375,
%U A079484 2500100833531245335015625,1687568062633590601135546875
%N A079484 a(n)=(2n-1)!!*(2n+1)!!, where the double factorial is A000165.
%C A079484 a(n)=determinant of M(2n-1) where M(k) is the k X k matrix with m(i,j)=j 
               if i+j=k m(i,j)=i otherwise.
%C A079484 (-1)^n*a(n)/2^(2n-1) is the permanent of the (m x m) matrix {1/(x_i-y_j), 
               1<=i<=m, 1<=j<=m}, where x_1,x_2,...,x_m are the zeros of x^m-1 and 
               y_1,y_2,...,y_m the zeros of y^m+1 and m=2n-1.
%H A079484 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Struvefunction.html">Struve function</a>
%H A079484 G.-N. Han and C. Krattenthaler, <a href="http://arXiv.org/abs/math.RA/
               0003072">Rectangular Scott-type permanents</a>
%F A079484 a(n+1)=(4n^2-1)*a(n)
%F A079484 E.g.f.: 1/(1-x^2)^(3/2) (with interpolated zeros). - Paul Barry (pbarry(AT)wit.ie), 
               May 26 2003
%F A079484 (2n-1)! * C(2n-2, n-1) / 2^(2n-2). - R. Stephan, Mar 22 2004.
%F A079484 Alternatingly signed values have e.g.f. sqrt(1+x^2).
%F A079484 a(n) is the value of the n-th moment of : 1/Pi BesselK(1, sqrt(x)) on 
               the positive part of the real line. [From Olivier GERARD (olivier.gerard(AT)gmail.com), 
               May 20 2009]
%e A079484 M(5) is /1, 2, 3, 1, 5/ 1, 2, 2, 4, 5/ 1, 3, 3, 4, 5/ 4, 2, 3, 4, 5/ 
               1, 2, 3, 4, 5/
%e A079484 int( x^3 besselK(1, sqrt(x)), x=0..infty) = 1575 Pi. [From Olivier GERARD 
               (olivier.gerard(AT)gmail.com), May 20 2009]
%Y A079484 Cf. A001818, A000165.
%Y A079484 Bisection of A000246, A053195, |A013069|, |A046126|. Cf. A000909.
%Y A079484 Cf. A001044, A010791, |A129464|, A114779, are also values of similar 
               moments. [From Olivier GERARD (olivier.gerard(AT)gmail.com), May 
               20 2009]
%Y A079484 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 27 
               2009: (Start)
%Y A079484 Equals the row sums of A162005.
%Y A079484 (End)
%Y A079484 Sequence in context: A144949 A144950 A144951 this_sequence A012494 A012780 
               A072503
%Y A079484 Adjacent sequences: A079481 A079482 A079483 this_sequence A079485 A079486 
               A079487
%K A079484 nonn
%O A079484 1,2
%A A079484 Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 17 2003
%E A079484 Simpler description from Daniel Flath (deflath(AT)yahoo.com), Mar 05 
               2004

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