OFFSET
0,4
FORMULA
T(n,k)=binomial(n,k+1).
Sum_{0<=k<=n} T(n,k)*x^k = ((x+1)^n-1)/x for n>0.
G.f.: (1-(1+y)*x+(1+y)*x^2)/(1-(2+y)*x+(1+y)*x^2).
T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - T(n-2,k) - T(n-2,k-1), T(0,0) = T(1,0) = T(2,1) = 1, T(1,1) = T(2,2) = 0, T(2,0) = 2, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Feb 12 2014
EXAMPLE
Triangle begins :
1
1, 0
2, 1, 0
3, 3, 1, 0
4, 6, 4, 1, 0
5, 10, 10, 5, 1, 0
6, 15, 20, 15, 6, 1, 0
CROSSREFS
KEYWORD
AUTHOR
Philippe Deléham, Nov 01 2011
STATUS
approved