OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Elena Barcucci, Vincent Vajnovszki, Generalized Schroeder permutations, Theoretical Computer Science, Volume 502, 2 September 2013, Pages 210-216.
FORMULA
Generating function: (1+2*x+3*x*(-x+1-(1-6*x+x^2)^(1/2))/(x+(1-6*x+x^2)^(1/2)))*x.
Recurrence (for n>=5): (n-2)*a(n) = 3*(4*n - 11)*a(n-1) - (37*n - 131)*a(n-2) + 6*(n-5)*a(n-3). - Vaclav Kotesovec, Nov 20 2012
a(n) ~ 3*sqrt(3*sqrt(2)-4)*(3+2*sqrt(2))^n/(n^(3/2)*sqrt(Pi)). - Vaclav Kotesovec, Nov 20 2012
MATHEMATICA
CoefficientList[Series[x(1 + 2x + 3x(-x + 1 - (1 - 6x + x^2)^(1/2))/(x + (1 - 6x + x^2)^(1/2))), {x, 0, 23}], x] (* Robert G. Wilson v, Jun 28 2010 *)
PROG
(PARI) x='x+O('x^50); concat([0], Vec((1+2*x+3*x*(-x+1-(1-6*x+x^2)^(1/2))/(x+(1-6*x+x^2)^(1/2)))*x)) \\ G. C. Greubel, Mar 24 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vincent Vajnovszki (vvajnov(AT)u-bourgogne.fr), May 30 2010
EXTENSIONS
a(19) onward from Robert G. Wilson v, Jun 28 2010
STATUS
approved