OFFSET
0,5
COMMENTS
FORMULA
a(n, m) = A060098(2*n-m, m).
a(n, m) = Sum_{j=0..floor((m+1)/2)} binomial((n-m)-j+2*m, 2*m)*binomial(m+1, 2*j), n >= m >= 0, otherwise zero.
G.f. for column m: (x^m)*Pe(m+1, x)/(1-x)^(2*m+1), with Pe(n, x) = Sum_{j=0..floor(n/2)} binomial(n, 2*j)*x^j (even members of row n of Pascal triangle A007318).
EXAMPLE
{1}; {1,1}; {1,4,1}; {1,9,8,1}; ... Pe(3,x) = 1 + 3*x.
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Apr 06 2001
STATUS
approved