OFFSET
0,2
COMMENTS
Triangle T(n,k), read by rows, given by (2, 3, 5, 6, 8, 9, 11, 12, 14, ... (A007494)) DELTA (3, 0, 3, 0, 3, 0, 3, 0, 3, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, May 15 2015
LINKS
Peter Luschny, Generalized Eulerian polynomials.
Peter Luschny, The Stirling-Frobenius numbers.
FORMULA
For a recurrence see the Sage program.
T(n,k) = 3^k * A225470(n,k). - Philippe Deléham, May 14 2015.
EXAMPLE
[n\k][ 0, 1, 2, 3, 4, 5, 6 ]
[0] 1,
[1] 2, 3,
[2] 10, 21, 9,
[3] 80, 198, 135, 27,
[4] 880, 2418, 2079, 702, 81,
[5] 12320, 36492, 36360, 16065, 3240, 243,
[6] 209440, 657324, 727596, 382185, 103275, 13851, 729.
MATHEMATICA
s[_][0, 0] = 1; s[m_][n_, k_] /; (k > n || k < 0) = 0; s[m_][n_, k_] := s[m][n, k] = s[m][n - 1, k - 1] + (m*n - 1)*s[m][n - 1, k];
T[n_, k_] := 3^k*s[3][n, k];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Jean-François Alcover, Aug 02 2019 *)
PROG
(Sage)
@CachedFunction
def SF_CS(n, k, m):
if k > n or k < 0 : return 0
if n == 0 and k == 0: return 1
return m*SF_CS(n-1, k-1, m) + (m*n-1)*SF_CS(n-1, k, m)
for n in (0..8): [SF_CS(n, k, 3) for k in (0..n)]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, May 17 2013
STATUS
approved