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, 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

Author

Peter Luschny, Aug 13 2019

Keywords

• nonn
• tabl

Comments

Rows converge to the main diagonal A327006.

Examples

			[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, ...
		

Links

• Peter Luschny, The Bell transform.
• J. Riordan, Letter, Jul 06 1978.

Crossrefs

A005046 is a bisection of row 2. Main diagonal is A327006.

Cf. A264428.

Programs

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);