OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Dan Daly and Lara Pudwell, Pattern avoidance in rook monoids, Special Session on Patterns in Permutations and Words, Joint Mathematics Meetings, 2013.
FORMULA
From Vaclav Kotesovec, Feb 07 2013: (Start)
E.g.f.: 1/2*(exp(2*x)*BesselI(0,2*x)+1)/(1-x).
Recurrence: n*a(n) = (n^2+4*n-2)*a(n-1)-2*(n-1)*(2*n-1)*a(n-2).
a(n) ~ c * n!, where c = (exp(2)*BesselI(0,2)+1)/2 = 8.921991840629494...
(End)
c = 1 + Sum_{k>=0} binomial(2*k+1,k) / (k+1)!. - Vaclav Kotesovec, Jul 19 2021
MATHEMATICA
CoefficientList[Series[1/2*(Exp[2*x]*BesselI[0, 2*x]+1)/(1-x), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Feb 07 2013 *)
PROG
(PARI) a(n) = {sum(k=0, n, if (k==n, n!, sum(j=1, k+1, binomial(n-j, n-k-1)*binomial(n, k)*binomial(k, j-1)*(j-1)!))); } \\ Michel Marcus, Feb 07 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 04 2013
EXTENSIONS
More terms from Michel Marcus, Feb 07 2013
STATUS
approved