OFFSET
0,5
COMMENTS
LINKS
P. Barry, A Note on a Family of Generalized Pascal Matrices Defined by Riordan Arrays, Journal of Integer Sequences, 16 (2013), #13.5.4.
FORMULA
T(n, k) = Sum_{j=0..n} C(n, j)*C(k, j-k)2^(j-k).
T(n, k) = Sum_{j=0..n-k} C(k, j)*C(n+k-j, 2k).
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(1,1)=1, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Jan 11 2014
G.f.: 1/(1-y-x*(1+y)/(1-y)). - Vladimir Kruchinin, Apr 21 2015
EXAMPLE
Triangle begins
1;
1, 1;
1, 4, 1;
1, 9, 7, 1;
1, 16, 26, 10, 1;
1, 25, 70, 52, 13, 1;
1, 36,155,190, 87, 16, 1;
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Nov 16 2005
STATUS
approved