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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.
1
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, 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, 422, 1394, 0, 0, 1, 0, 1, 2, 6, 24, 105, 505, 2201, 5476, 6556, 0
OFFSET
1,19
COMMENTS
Rows converge to the main diagonal A327006.
EXAMPLE
[1] 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
[2] 1, 0, 1, 0, 4, 0, 31, 0, 379, 0, 6556, 0, ...
[3] 1, 0, 1, 2, 3, 21, 57, 231, 1394, 5476, 32616, 203105, ...
[4] 1, 0, 1, 2, 6, 20, 101, 422, 2201, 12560, 76846, 483892, ...
[5] 1, 0, 1, 2, 6, 24, 100, 505, 2620, 15383, 97480, 657305, ...
[6] 1, 0, 1, 2, 6, 24, 105, 504, 2759, 16186, 103494, 710384, ...
MAPLE
# BellMatrix is defined in A264428.
T := proc(n, k) BellMatrix(x -> modp(x, n), k): add(i, i in %[k]) end:
seq(seq(T(n-k+1, k), k=1..n), n=1..12);
CROSSREFS
A005046 is a bisection of row 2. Main diagonal is A327006.
Cf. A264428.
Sequence in context: A072068 A078145 A348892 * A300858 A276995 A074078
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Aug 13 2019
STATUS
approved