A264433 Triangle read by rows, Bell transform of the third-order Bell numbers, T(n,k) for n >= 0 and 0 <= k <= n.

1, 0, 1, 0, 1, 1, 0, 2, 3, 1, 0, 6, 11, 6, 1, 0, 24, 50, 35, 10, 1, 0, 119, 274, 225, 85, 15, 1, 0, 700, 1757, 1624, 735, 175, 21, 1, 0, 4748, 12880, 13104, 6769, 1960, 322, 28, 1, 0, 36403, 106068, 117152, 67200, 22449, 4536, 546, 36, 1, 0, 310851, 968206, 1150050, 720020, 269115, 63273, 9450, 870, 45, 1

Offset: 0

Author

Peter Luschny, Dec 02 2015

Keywords

• nonn
• tabl

Examples

			[1]
[0,     1]
[0,     1,      1]
[0,     2,      3,      1]
[0,     6,     11,      6,     1]
[0,    24,     50,     35,    10,     1]
[0,   119,    274,    225,    85,    15,    1]
[0,   700,   1757,   1624,   735,   175,   21,   1]
[0,  4748,  12880,  13104,  6769,  1960,  322,  28,  1]
[0, 36403, 106068, 117152, 67200, 22449, 4536, 546, 36, 1]
		

Crossrefs

Cf. A000110, A048993, A264428, A264430.

Programs

Sage

# uses[bell_transform from A264428]
def A264433_triangle(dim):
    uno = [1]*dim
    bell_number = [sum(bell_transform(n, uno)) for n in range(dim)]
    bell_number_2 = [sum(bell_transform(n, bell_number)) for n in range(dim)]
    bell_number_3 = [sum(bell_transform(n, bell_number_2)) for n in range(dim)]
    for n in range(dim): print(bell_transform(n, bell_number_3))
A264433_triangle(10)

Extensions

More terms from Michel Marcus, Mar 27 2020