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A265604
Triangle read by rows: The inverse Bell transform of the quartic factorial numbers (A007696).
7
1, 0, 1, 0, 1, 1, 0, -2, 3, 1, 0, 10, -5, 6, 1, 0, -80, 30, -5, 10, 1, 0, 880, -290, 45, 5, 15, 1, 0, -12320, 3780, -560, 35, 35, 21, 1, 0, 209440, -61460, 8820, -735, 0, 98, 28, 1, 0, -4188800, 1192800, -167300, 14700, -735, 0, 210, 36, 1
OFFSET
0,8
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, -2, 3, 1]
[ 0, 10, -5, 6, 1]
[ 0, -80, 30, -5, 10, 1]
[ 0, 880, -290, 45, 5, 15, 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_4_1 = lambda n: prod(4*k + 1 for k in (0..n-1))
print(inverse_bell_matrix(multifact_4_1, 8))
CROSSREFS
Inverse Bell transforms of other multifactorials are: A048993, A049404, A049410, A075497, A075499, A075498, A119275, A122848, A265605.
Sequence in context: A296455 A383656 A137329 * A171996 A175669 A288839
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Dec 30 2015
STATUS
approved