OFFSET
0,4
LINKS
Alois P. Heinz, Rows n = 0..140, flattened
FORMULA
Sum_{k=0..n} (k+1) * T(n,k) = A040027(n+1). - Alois P. Heinz, Dec 02 2023
EXAMPLE
Triangle begins:
1;
1, 1;
2, 2, 1;
5, 5, 4, 1;
15, 15, 13, 8, 1;
52, 52, 47, 35, 16, 1;
203, 203, 188, 153, 97, 32, 1;
877, 877, 825, 706, 515, 275, 64, 1;
4140, 4140, 3937, 3479, 2744, 1785, 793, 128, 1;
21147, 21147, 20270, 18313, 15177, 11002, 6347, 2315, 256, 1;
115975, 115975, 111835, 102678, 88033, 68303, 45368, 23073, 6817, 512, 1;
...
MAPLE
T:= (n, k)-> add(Stirling2(n-k, j)*(j+1)^k, j=0..n-k):
seq(seq(T(n, k), k=0..n), n=0..10); # Alois P. Heinz, Dec 01 2023
MATHEMATICA
A362925[n_, m_]:=Sum[StirlingS2[n-m, k](k+1)^m, {k, 0, n-m}];
Table[A362925[n, m], {n, 0, 15}, {m, 0, n}] (* Paolo Xausa, Dec 04 2023 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Aug 10 2023, based on an email from Don Knuth.
STATUS
approved