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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 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] MATHEMATICA (*  The function BellMatrix is defined in A264428 *) nmax = 8; M = BellMatrix[1/(# + 1)&, nmax + 1]; B[n_, k_] := M[[n + 1, k + 1]]; T[n_, k_] := n! B[n, k]; Table[T[n, k], {n, 0, nmax}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 12 2019 *) PROG (Sage) # uses[bell_transform from 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: A259356 A137302 A324305 * A332628 A091518 A096734 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 September 28 06:57 EDT 2021. Contains 347703 sequences. (Running on oeis4.)