A129890 a(n) = (2*n+2)!! - (2*n+1)!!.

1, 5, 33, 279, 2895, 35685, 509985, 8294895, 151335135, 3061162125, 68000295825, 1645756410375, 43105900812975, 1214871076343925, 36659590336994625, 1179297174137457375, 40288002704636061375, 1456700757237661060125

Offset

0,2

Comments

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.

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]

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

Links

Table of n, a(n) for n=0..17.

Selden Crary, Richard Diehl Martinez, Michael Saunders, The Nu Class of Low-Degree-Truncated Rational Multifunctions. Ib. Integrals of Matern-correlation functions for all odd-half-integer class parameters, arXiv:1707.00705 [stat.ME], 2017, Table 2.

Alexander Kreinin, Integer Sequences and Laplace Continued Fraction, Preprint 2016.

Alexander Kreinin, Integer Sequences Connected to the Laplace Continued Fraction and Ramanujan's Identity, Journal of Integer Sequences, 19 (2016), #16.6.2.

N. Ochiumi, On the total sum of number of nodes covering a given number of leaves in an unordered binary tree

Donovan Young, A critical quartet for queuing couples, arXiv:2007.13868 [math.CO], 2020.

Formula

E.g.f.: 2/((1-2*x)^2)-1/[(1-2*x)*sqrt(1-2*x)]. - Sergei N. Gladkovskii, Dec 04 2011

a(n) = (2n+1)*a(n-1) + A000165(n). - Philippe Deléham, Oct 28 2013

Example

2!! - 1!! =  2 -  1 =  1;
4!! - 3!! =  8 -  3 =  5;
6!! - 5!! = 48 - 15 = 33.

Maple

seq(doublefactorial(2*n+2)-doublefactorial(2*n+1), n=0..9); # Peter Luschny, Dec 01 2014

Mathematica

a[n_] := (2n+2)!! - (2n+1)!!;
Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Jul 30 2018 *)

Crossrefs

Cf. A006882, A122649, A202212, A336599.

Sequence in context: A215671 A049377 A325153 * A316158 A120733 A218496

Adjacent sequences: A129887 A129888 A129889 * A129891 A129892 A129893

Keyword

easy,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Jun 04 2007

Extensions

New name from Peter Luschny, Dec 01 2014

Status

approved