OFFSET
0,5
COMMENTS
Also the Bell transform of A000262(n+1). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 29 2016
EXAMPLE
Triangle starts:
1;
0, 1;
0, 3, 1;
0, 13, 9, 1;
0, 73, 79, 18, 1;
0, 501, 755, 265, 30, 1;
0, 4051, 7981, 3840, 665, 45, 1;
MAPLE
# The function BellMatrix is defined in A264428.
BellMatrix(n -> simplify(hypergeom([-n, -n-1], [], 1)), 9); # Peter Luschny, Jan 29 2016
MATHEMATICA
BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
B = BellMatrix[Function[n, HypergeometricPFQ[{-n, -n-1}, {}, 1]], rows = 12];
Table[B[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 28 2018, after Peter Luschny *)
PROG
def Lah(n, k):
if n == k: return 1
if k<0 or k>n: return 0
return (k*n*gamma(n)^2)/(gamma(k+1)^2*gamma(n-k+1))
matrix(ZZ, 8, Lah) * matrix(ZZ, 8, stirling_number2) # as a square matrix
CROSSREFS
KEYWORD
AUTHOR
Peter Luschny, Apr 12 2015
STATUS
approved