OFFSET
0,2
FORMULA
Moment representation: a(n) = (1/Pi)*Integral_{x = 4..8} (x^n*sqrt((8 - x)*(x - 4))/(x*(4 - x)) dx + sqrt(2)*0^n;
Also a(n) = C(2*n, n) - Sum_{k = 1..n} 2^(k+1)*C(2*k-2, k-1)*C(2*n-2*k, n-k)/k.
From Peter Bala, Feb 03 2024: (Start)
a(n) = - 2*A104498(n) for n >= 1.
G.f: c(-x/(1 - 8*x)) / c(x/(1 - 4*x)), where c(x) = (1 - sqrt(1 - 4*x))/(2*x) is the g.f. of the Catalan numbers A000108.
P-recursive: n*a(n) = (12*n - 14)*a(n-1) - 32*(n - 2)*a(n-2) with a(0) = 1 and a(1) = -2. (End)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Mar 11 2005, Mar 07 2008
STATUS
approved