OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n)= A113647(n+5, n+1), n>=0.
G.f.: ((-2 + 16*x - 24*x^2 + x^5) + 2*(1 - 10*x + 24*x^2 - 8*x^3)*c(2*x))/((x^5)*(1+x)), with the o.g.f. c(x):=(1-sqrt(1-4*x))/(2*x) of A000108 (Catalan numbers).
Recurrence: (n-1)*(n+6)*a(n) = (7*n^2+23*n+30)*a(n-1) + 4*(n+2)*(2*n+3)*a(n-2). - Vaclav Kotesovec, Oct 19 2012
a(n) ~ 7*2^(3n+13)/(9*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 19 2012
MATHEMATICA
CoefficientList[Series[((-2+16*x-24*x^2+x^5)+2*(1-10*x+24*x^2-8*x^3)*(1-Sqrt[1-8*x])/(4*x))/((x^5)*(1+x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jan 13 2006
STATUS
approved