A257566 Triangle read by rows, T(n,k) = Sum_{j=0..n-k+1} P(n,j)*T(n-j,k-1) if k>0 else 0^n where P(n,j) is the number of j-partitions of n; for n>=0 and 0<=k<=n.

1, 0, 1, 0, 2, 1, 0, 3, 4, 1, 0, 5, 13, 7, 1, 0, 7, 30, 30, 10, 1, 0, 11, 76, 119, 65, 14, 1, 0, 15, 152, 357, 306, 113, 18, 1, 0, 22, 330, 1119, 1375, 746, 193, 23, 1, 0, 30, 633, 2973, 5059, 3888, 1497, 295, 28, 1, 0, 42, 1245, 8036, 18605, 19423, 10298, 2930, 447, 34, 1

Offset: 0

Author

Peter Luschny, Apr 30 2015

Keywords

• nonn
• tabl
• easy

Examples

			1;
0,  1;
0,  2,  1;
0,  3,  4,   1;
0,  5, 13,   7,  1;
0,  7, 30,  30, 10,  1;
0, 11, 76, 119, 65, 14, 1;
		

Crossrefs

Cf. A000041, A014616.

Programs

Maple

T := proc(n,k) option remember; `if`(k=0, 0^n,
add(combinat:-numbpart(n,j)*T(n-j, k-1), j=0..n-k+1)) end:
for n from 0 to 12 do seq(T(n, k), k=0..n) od;

Formula

T(n,1) = A000041(n) for n>=1.

T(n,n-1) = A014616(n-1) for n>=2.