OFFSET
1,4
LINKS
Toufik Mansour and Mark Shattuck, Counting set partitions by the number of movable letters, Journal of Difference Equations and Applications, 26:3, 384-403, (2020). On ResearchGate. See Theorem 8.
FORMULA
EXAMPLE
Triangle begins:
0;
1, 0;
2, 4, 0;
3, 17, 9, 0;
4, 52, 68, 16, 0;
5, 139, 345, 190, 25, 0;
...
MATHEMATICA
T[n_, k_]:=If[k==1, n-1, (2n-1)StirlingS2[n, k]/2-StirlingS2[n+1, k]/2+StirlingS2[n-1, k-2]/2]; Table[T[n, k], {n, 10}, {k, n}]//Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Nov 19 2023
STATUS
approved