A269951 Triangle read by rows, T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(-j,-n)*S1(j,k), S1 the Stirling cycle numbers A132393, for n>=0 and 0<=k<=n.
1, 0, 1, 0, 2, 1, 0, 5, 5, 1, 0, 16, 23, 9, 1, 0, 65, 116, 65, 14, 1, 0, 326, 669, 470, 145, 20, 1, 0, 1957, 4429, 3634, 1415, 280, 27, 1, 0, 13700, 33375, 30681, 14084, 3535, 490, 35, 1, 0, 109601, 283072, 284066, 147532, 43939, 7756, 798, 44, 1
Offset: 0
Examples
Triangle begins: 1; 0, 1; 0, 2, 1; 0, 5, 5, 1; 0, 16, 23, 9, 1; 0, 65, 116, 65, 14, 1; 0, 326, 669, 470, 145, 20, 1;
Links
- Peter Luschny, Extensions of the binomial