OFFSET
0,2
COMMENTS
The probability that the middle card is not selected in a random draw of 2n consecutive card pairs between 4n + 1 cards is a(n)/(4n)!!.
Essentially a bisection of A001757. - Giovanni Resta, Mar 14 2017
LINKS
Ignacio Larrosa, El as de corazones
FORMULA
n*a(n) -2*(2*n-1)^3*a(n-1)=0. - R. J. Mathar, Jul 15 2017
EXAMPLE
For n = 1, you have 5 cards (A, B, C, D, E) and you can make 2 draws of pairs of consecutive cards (AB, DE) and (DE, AB) without select C.
MAPLE
ogf := sqrt(x) * BesselI(0, sqrt(x)/4) * BesselK(0, sqrt(x)/4) / 2;
simplify(subs(x=1/x, asympt(ogf, x, 20))); # Mark van Hoeij, Oct 24 2017
MATHEMATICA
Table[Binomial[2n, n] Product[2n + 1 - 2i, {i, 1, n}]^2, {n, 0, 15}] (* Indranil Ghosh, Mar 22 2017 *)
PROG
(PARI) a(n)=binomial(2*n, n)*prod(i=1, n, 2*n+1-2*i)^2 \\ Charles R Greathouse IV, Mar 14 2017
(Python)
from sympy import binomial, factorial2
print([binomial(2*n, n) * factorial2(2*n - 1)**2 for n in range(15)]) # Indranil Ghosh, Mar 22 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ignacio Larrosa CaƱestro, Mar 14 2017
STATUS
approved