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A265605 Triangle read by rows: The inverse Bell transform of the triple factorial numbers 3^n*n! (A032031). 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

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,   -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

Cf. A032031, A264428, A264429.

Inverse Bell transforms of other multifactorials are: A048993, A049404, A049410, A075497, A075499, A075498, A119275, A122848, A265604.

Sequence in context: A058600 A133704 A160019 * A035629 A099546 A036870

Adjacent sequences:  A265602 A265603 A265604 * A265606 A265607 A265608

KEYWORD

sign,tabl

AUTHOR

Peter Luschny, Dec 30 2015

STATUS

approved

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Last modified May 17 16:03 EDT 2021. Contains 343980 sequences. (Running on oeis4.)