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%I #55 Aug 11 2020 07:20:48
%S 1,5,33,279,2895,35685,509985,8294895,151335135,3061162125,
%T 68000295825,1645756410375,43105900812975,1214871076343925,
%U 36659590336994625,1179297174137457375,40288002704636061375,1456700757237661060125
%N a(n) = (2*n+2)!! - (2*n+1)!!.
%C Previous name was: Difference between the double factorial of the n-th nonnegative even number and the double factorial of the n-th nonnegative odd number.
%C In other words, a(n) = b(2n+2)-b(2n+1), where b = A006882. - _N. J. A. Sloane_, Dec 14 2011 [Corrected _Peter Luschny_, Dec 01 2014]
%C a(n) is the number of linear chord diagrams on 2n+2 vertices with one marked chord such that none of the remaining n chords are contained within the marked chord, see [Young]. - _Donovan Young_, Aug 11 2020
%H Selden Crary, Richard Diehl Martinez, Michael Saunders, <a href="https://arxiv.org/abs/1707.00705">The Nu Class of Low-Degree-Truncated Rational Multifunctions. Ib. Integrals of Matern-correlation functions for all odd-half-integer class parameters</a>, arXiv:1707.00705 [stat.ME], 2017, Table 2.
%H Alexander Kreinin, <a href="https://www.researchgate.net/profile/Alexander_Kreinin/publication/294260037">Integer Sequences and Laplace Continued Fraction</a>, Preprint 2016.
%H Alexander Kreinin, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Kreinin/kreinin4.html">Integer Sequences Connected to the Laplace Continued Fraction and Ramanujan's Identity</a>, Journal of Integer Sequences, 19 (2016), #16.6.2.
%H N. Ochiumi, <a href="http://infoshako.sk.tsukuba.ac.jp/~hachi/COS/cos2011/abst/ochiumi.pdf">On the total sum of number of nodes covering a given number of leaves in an unordered binary tree</a>
%H Donovan Young, <a href="https://arxiv.org/abs/2007.13868">A critical quartet for queuing couples</a>, arXiv:2007.13868 [math.CO], 2020.
%F E.g.f.: 2/((1-2*x)^2)-1/[(1-2*x)*sqrt(1-2*x)]. - _Sergei N. Gladkovskii_, Dec 04 2011
%F a(n) = (2n+1)*a(n-1) + A000165(n). - _Philippe Deléham_, Oct 28 2013
%e 2!! - 1!! = 2 - 1 = 1;
%e 4!! - 3!! = 8 - 3 = 5;
%e 6!! - 5!! = 48 - 15 = 33.
%p seq(doublefactorial(2*n+2)-doublefactorial(2*n+1),n=0..9); # _Peter Luschny_, Dec 01 2014
%t a[n_] := (2n+2)!! - (2n+1)!!;
%t Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Jul 30 2018 *)
%Y Cf. A006882, A122649, A202212, A336599.
%K easy,nonn
%O 0,2
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Jun 04 2007
%E New name from _Peter Luschny_, Dec 01 2014
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