OFFSET
1,2
COMMENTS
LINKS
Wolfdieter Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
FORMULA
a(n+1, m) = 3*(3*n+m)*a(n, m)/(n+1) + m*a(n, m-1)/(n+1), n >= m >= 1; a(n, m) := 0, n<m; a(n, 0) := 0; a(1, 1)=1.
G.f. for column m: ((-1+(1-9*x)^(-1/3))/3)^m.
EXAMPLE
Triangle begins:
1,
6, 1;
42, 12, 1;
315, 120, 18, 1;
2457, 1134, 234, 24, 1;
19656, 10458, 2673, 384, 30, 1;
...
MATHEMATICA
a[n_, m_] /; n - 1 >= m >= 1 := (m*a[n - 1, m - 1])/n + (3*(m + 3*(n - 1))*a[n - 1, m])/n; a[n_, m_] /; n < m = 0; a[n_, 0] = 0; a[n_, n_] = 1; Flatten[Table[a[n, m], {n, 1, 9}, {m, 1, n}]] (* Jean-François Alcover, Jul 10 2012, from formula *)
CROSSREFS
KEYWORD
AUTHOR
STATUS
approved