OFFSET
0,8
FORMULA
EXAMPLE
Triangle begins:
1;
0, 1;
0, 1, 1;
0, 2, 3, 1;
0, 5, 8, 7, 1;
0, 14, 23, 26, 15, 1;
0, 42, 70, 89, 80, 31, 1;
0, 132, 222, 302, 335, 242, 63, 1;
0, 429, 726, 1032, 1294, 1265, 728, 127, 1;
MAPLE
T := (n, m) -> `if`(n=0, 1,
add(combinat[eulerian1](m, k-m)*binomial(2*n-k-1, n-k)*k/n, k=m..m+min(m, n-m))):
for n from 0 to 8 do seq(T(n, k), k=0..n) od; # Peter Luschny, Jan 26 2018
PROG
(Maxima)
T(n, m):=if n<m then 0 else if n=m then 1 else sum(k*k!*(-1)^(m+k)*stirling2(m, k)* binomial(2*n+k-2*m-1, n-m)/(n+k-m), k, 1, m);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Jan 26 2018
STATUS
approved