A394438 Triangle read by rows: The Bell-transform of the triangular numbers.

1, 0, 1, 0, 3, 1, 0, 6, 9, 1, 0, 10, 51, 18, 1, 0, 15, 230, 195, 30, 1, 0, 21, 900, 1635, 525, 45, 1, 0, 28, 3192, 11655, 6965, 1155, 63, 1, 0, 36, 10528, 74088, 77385, 22120, 2226, 84, 1, 0, 45, 32832, 432054, 757764, 350595, 57960, 3906, 108, 1

Offset

0,5

Links

Table of n, a(n) for n=0..54.

Peter Luschny, The Bell transform.

Peter Luschny, Examples of the Bell transform, a SageMath notebook.

Example

Triangle starts:
  [0] [1]
  [1] [0,  1]
  [2] [0,  3,     1]
  [3] [0,  6,     9,      1]
  [4] [0, 10,    51,     18,      1]
  [5] [0, 15,   230,    195,     30,      1]
  [6] [0, 21,   900,   1635,    525,     45,     1]
  [7] [0, 28,  3192,  11655,   6965,   1155,    63,    1]
  [8] [0, 36, 10528,  74088,  77385,  22120,  2226,   84,   1]
  [9] [0, 45, 32832, 432054, 757764, 350595, 57960, 3906, 108, 1]

Maple

BellMatrix(n -> iquo((n + 1)*(n + 2), 2), 10); # Function 'BellMatrix' defined in A264428.

Prog

(Python) # The function 'BellTransform' is defined in A394439.
N = 9; tri_nums = [n * (n + 1) // 2 for n in range(N + 1)]
T = BellTransform(tri_nums)
for row in T: print(row)

Crossrefs

Cf. A000217 (column 1), A279361 (row sums), A264428, A394439.

Sequence in context: A137651 A248826 A058152 * A393519 A058140 A074678

Adjacent sequences: A394435 A394436 A394437 * A394439 A394440 A394441

Keyword

nonn,tabl

Author

Peter Luschny, Mar 29 2026

Status

approved