OFFSET
1,4
COMMENTS
The recurrence given by Roselle is wrong.
LINKS
D. P. Roselle, Permutations by number of rises and successions, Proc. Amer. Math. Soc., 19 (1968), 8-16.
D. P. Roselle, Permutations by number of rises and successions, Proc. Amer. Math. Soc., 19 (1968), 8-16. [Annotated scanned copy]
FORMULA
EXAMPLE
Triangle begins:
1;
1;
1, 2;
1, 8, 2;
1, 22, 28, 2;
...
MATHEMATICA
a[_, 1] = 1; a[n_, 2] := 2^n - 2*n; a[n_, r_] /; 1 <= r <= n-1 := a[n, r] = r*a[n-1, r] + (n-r)*a[n-1, r-1] + (n-2)*a[n-2, r-1]; a[_, _] = 0;
row[1] = {{1}}; row[n_] := Table[a[n, r], {r, 1, n-1}];
Table[row[n], {n, 1, 11}] // Flatten (* Jean-François Alcover, Sep 07 2017 *)
CROSSREFS
KEYWORD
nonn,easy,nice,tabf
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Jan 03 2003
STATUS
approved