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A265607 Triangle read by rows, T(n,k) = n!*B(n,k) for n>=0 and 0<=k<=n, where B(n,k) is the Bell matrix with generator 1/j for j>=1. 2
1, 0, 1, 0, 1, 2, 0, 2, 9, 6, 0, 6, 50, 72, 24, 0, 24, 350, 850, 600, 120, 0, 120, 3014, 11250, 12900, 5400, 720, 0, 720, 31164, 170618, 286650, 191100, 52920, 5040, 0, 5040, 378888, 2962736, 6909784, 6585600, 2869440, 564480, 40320 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

See A264428 and the link for the definition of the Bell transform and the Bell matrix.

LINKS

Table of n, a(n) for n=0..44.

Peter Luschny, The Bell transform

EXAMPLE

[n\k 0    1      2       3       4       5     6     7]

[0] [1]

[1] [0,   1]

[2] [0,   1,     2]

[3] [0,   2,     9,      6]

[4] [0,   6,    50,     72,     24]

[5] [0,  24,   350,    850,    600,    120]

[6] [0, 120,  3014,  11250,  12900,   5400,   720]

[7] [0, 720, 31164, 170618, 286650, 191100, 52920, 5040]

PROG

(Sage)

# The function bell_transform is defined in A264428.

def A265607_row(n):

    invnat = [1/k for k in (1..n)]

    return [factorial(n)*b for b in bell_transform(n, invnat)]

[A265607_row(n) for n in range(9)]

CROSSREFS

Cf. A264428.

Sequence in context: A242052 A259356 A137302 * A091518 A096734 A220234

Adjacent sequences:  A265604 A265605 A265606 * A265608 A265609 A265610

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Dec 20 2015

STATUS

approved

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Last modified February 25 00:39 EST 2018. Contains 299630 sequences. (Running on oeis4.)