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%I #20 Mar 31 2022 22:00:07
%S 1,0,1,0,1,2,0,2,9,6,0,6,50,72,24,0,24,350,850,600,120,0,120,3014,
%T 11250,12900,5400,720,0,720,31164,170618,286650,191100,52920,5040,0,
%U 5040,378888,2962736,6909784,6585600,2869440,564480,40320
%N 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.
%C See A264428 and the link for the definition of the Bell transform and the Bell matrix.
%H Andreas B. G. Blobel, <a href="https://arxiv.org/abs/2203.09519">On convolution powers of 1/x</a>, arXiv:2203.09519 [math.CO], 2022.
%H Peter Luschny, <a href="https://oeis.org/wiki/User:Peter_Luschny/BellTransform">The Bell transform</a>
%e [n\k 0 1 2 3 4 5 6 7]
%e [0] [1]
%e [1] [0, 1]
%e [2] [0, 1, 2]
%e [3] [0, 2, 9, 6]
%e [4] [0, 6, 50, 72, 24]
%e [5] [0, 24, 350, 850, 600, 120]
%e [6] [0, 120, 3014, 11250, 12900, 5400, 720]
%e [7] [0, 720, 31164, 170618, 286650, 191100, 52920, 5040]
%t (* The function BellMatrix is defined in A264428 *)
%t nmax = 8;
%t M = BellMatrix[1/(# + 1)&, nmax + 1];
%t B[n_, k_] := M[[n + 1, k + 1]];
%t T[n_, k_] := n! B[n, k];
%t Table[T[n, k], {n, 0, nmax}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jul 12 2019 *)
%o (Sage) # uses[bell_transform from A264428]
%o def A265607_row(n):
%o invnat = [1/k for k in (1..n)]
%o return [factorial(n)*b for b in bell_transform(n, invnat)]
%o [A265607_row(n) for n in range(9)]
%Y Cf. A264428.
%K nonn,tabl
%O 0,6
%A _Peter Luschny_, Dec 20 2015
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