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
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
KEYWORD
easy,nonn
AUTHOR
Paolo P. Lava and Giorgio Balzarotti, Jun 04 2007
EXTENSIONS
New name from Peter Luschny, Dec 01 2014
STATUS
approved