VOOZH about

URL: https://oeis.org/A265605

⇱ A265605 - OEIS

login
A265605
Triangle read by rows: The inverse Bell transform of the triple factorial numbers (A007559).
6
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, 0, 10395, -3465, 490, -35, 70, 154, 28, 1, 0, -135135, 45045, -6895, 630, -105, 378, 294, 36, 1
OFFSET
0,9
LINKS
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.
Peter Luschny, The Bell transform
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
(SageMath) # 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
Inverse Bell transforms of other multifactorials are: A048993, A049404, A049410, A075497, A075499, A075498, A119275, A122848, A265604.
Sequence in context: A160019 A389657 A227054 * A035629 A099546 A036870
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Dec 30 2015
STATUS
approved