A265608 Triangle read by rows: Bell transform of A000262.

1, 0, 1, 0, 1, 1, 0, 3, 3, 1, 0, 13, 15, 6, 1, 0, 73, 95, 45, 10, 1, 0, 501, 723, 390, 105, 15, 1, 0, 4051, 6405, 3843, 1190, 210, 21, 1, 0, 37633, 64615, 42462, 14693, 3010, 378, 28, 1, 0, 394353, 730359, 519993, 197442, 45423, 6678, 630, 36, 1

Offset: 0

Author

Peter Luschny, Dec 20 2015

Keywords

• nonn
• tabl

Comments

See A264428 and the link for the definition of the Bell transform.

Examples

			[n\k 0      1      2      3      4     5    6   7  8]
[0] [1]
[1] [0,     1]
[2] [0,     1,     1]
[3] [0,     3,     3,     1]
[4] [0,    13,    15,     6,     1]
[5] [0,    73,    95,    45,    10,    1]
[6] [0,   501,   723,   390,   105,   15,   1]
[7] [0,  4051,  6405,  3843,  1190,  210,  21,  1]
[8] [0, 37633, 64615, 42462, 14693, 3010, 378, 28, 1]
		

Links

• Peter Luschny, The Bell transform

Crossrefs

Cf. A000262, A264428.

Programs

Sage

# uses[bell_transform from A264428]
def A265608_row(n):
    fact = [factorial(k) for k in (1..n)]
    fact2 = [sum(bell_transform(k, fact)) for k in range(n)]
    return bell_transform(n, fact2)
[A265608_row(n) for n in (0..9)]