

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
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OFFSET

0,8


LINKS

Table of n, a(n) for n=0..54.
Peter Luschny, The Bell transform
Richell O. Celeste, Roberto B. Corcino, 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

(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]*(dimn1) for n in srange(dim)]).inverse()
return matrix(ZZ, dim, lambda n, k: (1)^(nk)*M[n, k])
multifact_4_1 = lambda n: prod(4*k + 1 for k in (0..n1))
print(inverse_bell_matrix(multifact_4_1, 8))


CROSSREFS

Cf. A007696, A264428, A264429.
Inverse Bell transforms of other multifactorials are: A048993, A049404, A049410, A075497, A075499, A075498, A119275, A122848, A265605.
Sequence in context: A121434 A296455 A137329 * A171996 A175669 A288839
Adjacent sequences: A265601 A265602 A265603 * A265605 A265606 A265607


KEYWORD

sign,tabl


AUTHOR

Peter Luschny, Dec 30 2015


STATUS

approved



