OFFSET
0,9
LINKS
Peter Luschny, The Bell transform
Richell O. Celeste, Roberto B. Corcino, and Ken Joffaniel M. Gonzales, Two Approaches to Normal Order Coefficients, Journal of Integer Sequences, Vol. 20 (2017), Article 17.3.5.
EXAMPLE
[ 1]
[ 0, 1]
[ 0, 1, 1]
[ 0, -1, 3, 1]
[ 0, 3, -1, 6, 1]
[ 0, -15, 5, 5, 10, 1]
[ 0, 105, -35, 0, 25, 15, 1]
[ 0, -945, 315, -35, 0, 70, 21, 1]
PROG
(Sage) # uses[bell_transform from A264428]
def inverse_bell_matrix(generator, dim):
G = [generator(k) for k in srange(dim)]
row = lambda n: bell_transform(n, G)
M = matrix(ZZ, [row(n)+[0]*(dim-n-1) for n in srange(dim)]).inverse()
return matrix(ZZ, dim, lambda n, k: (-1)^(n-k)*M[n, k])
multifact_3_1 = lambda n: prod(3*k + 1 for k in (0..n-1))
print(inverse_bell_matrix(multifact_3_1, 8))
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Dec 30 2015
STATUS
approved