cp's OEIS Frontend

A327005 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.

%I A327005 #10 Aug 13 2019 19:33:58
%S A327005 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 A327005 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 A327005 422,1394,0,0,1,0,1,2,6,24,105,505,2201,5476,6556,0
%N A327005 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 A327005 Rows converge to the main diagonal A327006.
%H A327005 Peter Luschny, <a href="https://oeis.org/wiki/User:Peter_Luschny/BellTransform">The Bell transform</a>.
%H A327005 J. Riordan, <a href="/A001850/a001850_2.pdf">Letter, Jul 06 1978</a>.
%e A327005 [1] 1, 0, 0, 0, 0,  0,   0,   0,    0,     0,      0,      0, ...
%e A327005 [2] 1, 0, 1, 0, 4,  0,  31,   0,  379,     0,   6556,      0, ...
%e A327005 [3] 1, 0, 1, 2, 3, 21,  57, 231, 1394,  5476,  32616, 203105, ...
%e A327005 [4] 1, 0, 1, 2, 6, 20, 101, 422, 2201, 12560,  76846, 483892, ...
%e A327005 [5] 1, 0, 1, 2, 6, 24, 100, 505, 2620, 15383,  97480, 657305, ...
%e A327005 [6] 1, 0, 1, 2, 6, 24, 105, 504, 2759, 16186, 103494, 710384, ...
%p A327005 # BellMatrix is defined in A264428.
%p A327005 T := proc(n, k) BellMatrix(x -> modp(x, n), k): add(i, i in %[k]) end:
%p A327005 seq(seq(T(n-k+1,k), k=1..n), n=1..12);
%Y A327005 A005046 is a bisection of row 2. Main diagonal is A327006.
%Y A327005 Cf. A264428.
%K A327005 nonn,tabl
%O A327005 1,19
%A A327005 _Peter Luschny_, Aug 13 2019