OFFSET
0,12
COMMENTS
From Wolfdieter Lang, Jun 25 2011: (Start)
In the Gessel and Viennot reference f(n,k) = a(n,k)/A065553(n,k), n>=0, k>=0.
(n+1)*f(n,k) = A(n+1,n-k), with Knuth's A(m,k) =
LINKS
Ira M. Gessel and X. G. Viennot, Determinants, paths and plane partitions, 1989, p. 27, eqn 12.2
FORMULA
sum(n>=0, k>=0, f(n, k)*t^k*x^(2*n+1)/(2*n+1)! ) is the expansion of (cosh(sqrt(1+4*t)*x/2)-cosh(x/2))/t/sinh(x/2).
a(n,k)=numerator(f(n,k)).
EXAMPLE
Triangle begins:
{1},
{0, 1},
{0, -1, 1},
{0, 1, -1, 1},
{0, -3, 3, -1, 1},
{0, 5, -5, 17, -2, 1}.
CROSSREFS
KEYWORD
AUTHOR
Wouter Meeussen, Dec 02 2001
STATUS
approved