OFFSET
0,3
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 0..799
B. E. Sagan, Pattern avoidance in set partitions, arxiv:math/0604292 [math.CO], 2006, Theorems 2.5 and 3.4.
FORMULA
a(n) = Sum_{i=0..n/2} binomial(n,2*i)*(2*i)!!.
a(n) - 2*a(n-1) - (n-1)*a(n-2) + (n-2)*a(n-3) = 0.
MAPLE
MATHEMATICA
Table[Sum[Binomial[n, 2 i] (2 i)!!, {i, 0, n}], {n, 0, 26}] (* Michael De Vlieger, Mar 09 2016 *)
PROG
(PARI) a(n)=my(b=1, df=1, t); sum(i=1, n\2, t+=2; b*=(n-t+2)*(n-t+1)/(t*(t-1)); df*=t; b*df)+1 \\ Charles R Greathouse IV, Mar 10 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Mar 09 2016
EXTENSIONS
False conjecture deleted by Colin Barker, Oct 13 2016
STATUS
approved