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A189849 a(0)=1, a(1)=0, a(n)=4*n*(n-1)*(a(n-1)+2*(n-1)*a(n-2)) 0
1, 0, 16, 384, 23040, 2088960, 278323200, 50969640960, 12290021130240, 3774394191052800, 1438421245702963200, 666120016990568448000, 368420070161105761075200, 239869937154980747988172800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The number of ways n couples can sit in rows of two seats with no person next to their partner.

a(n)/(2n)! gives the probability of this is and tends to exp(-1/2) as n tends to infinity.

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n)=(-2)^n*n!*hypergeom([ -n, 1/2],[],2)

a(n) = (n!)^2 times the coefficient of x^n in the expansion of exp(-2*x)/sqrt(1-4*x).

a(n) = 2^n*n!*A053871(n)

MAPLE

a:=n->(-2)^n*n!*sum((-1/2)^i*binomial(n, i)*(2*i)!/i!, i=0..n):seq(a(j), j=1..20)

MATHEMATICA

Table[(-2)^n*n!*Sum[(-1/2)^i*Binomial[n, i]*(2*i)!/i!, {i, 0, n}], {n, 1, 20}]

RecurrenceTable[{a[0]==1, a[1]==0, a[n]==4n(n-1)(a[n-1]+2(n-1)a[n-2])}, a, {n, 20}] (* Harvey P. Dale, May 02 2012 *)

PROG

(Maxima) a[0]:1$ a[1]:0$ a[n]:=4*n*(n-1)*(a[n-1]+2*(n-1)*a[n-2])$ makelist(a[n], n, 0, 13);  [Bruno Berselli, May 23 2011]

CROSSREFS

Cf. A053871.

Sequence in context: A116166 A034976 A114426 * A051360 A227390 A284854

Adjacent sequences:  A189846 A189847 A189848 * A189850 A189851 A189852

KEYWORD

nonn,easy

AUTHOR

Stewart Herring, Apr 29 2011

STATUS

approved

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Last modified June 27 15:10 EDT 2017. Contains 288790 sequences.