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%I #10 Aug 13 2019 19:33:58
%S 1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,2,4,0,1,0,1,2,3,0,0,1,0,1,2,6,21,
%T 31,0,1,0,1,2,6,20,57,0,0,1,0,1,2,6,24,101,231,379,0,1,0,1,2,6,24,100,
%U 422,1394,0,0,1,0,1,2,6,24,105,505,2201,5476,6556,0
%N T(n, k) = Sum_{i=1..n} BM[k][i] where BM is the BellMatrix(x -> x mod n) as defined in A264428. Square array read by ascending antidiagonals for n >= 1 and k >= 1.
%C Rows converge to the main diagonal A327006.
%H Peter Luschny, <a href="https://oeis.org/wiki/User:Peter_Luschny/BellTransform">The Bell transform</a>.
%H J. Riordan, <a href="/A001850/a001850_2.pdf">Letter, Jul 06 1978</a>.
%e [1] 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e [2] 1, 0, 1, 0, 4, 0, 31, 0, 379, 0, 6556, 0, ...
%e [3] 1, 0, 1, 2, 3, 21, 57, 231, 1394, 5476, 32616, 203105, ...
%e [4] 1, 0, 1, 2, 6, 20, 101, 422, 2201, 12560, 76846, 483892, ...
%e [5] 1, 0, 1, 2, 6, 24, 100, 505, 2620, 15383, 97480, 657305, ...
%e [6] 1, 0, 1, 2, 6, 24, 105, 504, 2759, 16186, 103494, 710384, ...
%p # BellMatrix is defined in A264428.
%p T := proc(n, k) BellMatrix(x -> modp(x, n), k): add(i, i in %[k]) end:
%p seq(seq(T(n-k+1,k), k=1..n), n=1..12);
%Y A005046 is a bisection of row 2. Main diagonal is A327006.
%Y Cf. A264428.
%K nonn,tabl
%O 1,19
%A _Peter Luschny_, Aug 13 2019