This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A129890 #62 Jul 14 2025 00:15:22
%S A129890 1,5,33,279,2895,35685,509985,8294895,151335135,3061162125,
%T A129890 68000295825,1645756410375,43105900812975,1214871076343925,
%U A129890 36659590336994625,1179297174137457375,40288002704636061375,1456700757237661060125
%N A129890 a(n) = (2*n+2)!! - (2*n+1)!!.
%C A129890 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 A129890 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 A129890 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 A129890 Selden Crary, Richard Diehl Martinez, and 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 A129890 Alexander Kreinin, <a href="https://www.researchgate.net/profile/Alexander_Kreinin/publication/294260037">Integer Sequences and Laplace Continued Fraction</a>, Preprint 2016.
%H A129890 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 A129890 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 A129890 Donovan Young, <a href="https://arxiv.org/abs/2007.13868">A critical quartet for queuing couples</a>, arXiv:2007.13868 [math.CO], 2020.
%F A129890 E.g.f.: 2/((1-2*x)^2)-1/[(1-2*x)*sqrt(1-2*x)]. - _Sergei N. Gladkovskii_, Dec 04 2011
%F A129890 a(n) = (2*n+1)*a(n-1) + A000165(n). - _Philippe Deléham_, Oct 28 2013
%F A129890 Conjecture: a(n) = (2*n + 2)*(2*n + 2)! * Sum_{k >= 1} (-1)^(k+1)/Product_{j = 0..n+1} (k + 2*j). - _Peter Bala_, Jul 06 2025
%e A129890 2!! - 1!! = 2 - 1 = 1;
%e A129890 4!! - 3!! = 8 - 3 = 5;
%e A129890 6!! - 5!! = 48 - 15 = 33.
%p A129890 seq(doublefactorial(2*n+2)-doublefactorial(2*n+1),n=0..9); # _Peter Luschny_, Dec 01 2014
%t A129890 a[n_] := (2n+2)!! - (2n+1)!!;
%t A129890 Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Jul 30 2018 *)
%Y A129890 Cf. A006882, A122649, A202212, A336599.
%K A129890 easy,nonn
%O A129890 0,2
%A A129890 _Paolo P. Lava_ and _Giorgio Balzarotti_, Jun 04 2007
%E A129890 New name from _Peter Luschny_, Dec 01 2014