A264431 Triangle read by rows, inverse Bell transform of second order Bell numbers (A187761).

1, 0, 1, 0, -1, 1, 0, 1, -3, 1, 0, -1, 7, -6, 1, 0, 2, -15, 25, -10, 1, 0, -8, 37, -90, 65, -15, 1, 0, 27, -133, 322, -350, 140, -21, 1, 0, -70, 587, -1330, 1757, -1050, 266, -28, 1, 0, 265, -2526, 6607, -9114, 7077, -2646, 462, -36, 1

Offset: 0

Author

Peter Luschny, Nov 13 2015

Keywords

• sign
• tabl

Examples

			[ 1 ]
[ 0,     1 ]
[ 0,    -1,     1 ]
[ 0,     1,    -3,     1 ]
[ 0,    -1,     7,    -6,     1 ]
[ 0,     2,   -15,    25,   -10,     1 ]
[ 0,    -8,    37,   -90,    65,   -15,     1 ]
[ 0,    27,  -133,   322,  -350,   140,   -21,     1 ]
[ 0,   -70,   587, -1330,  1757, -1050,   266,   -28,     1 ]
[ 0,   265, -2526,  6607, -9114,  7077, -2646,   462,   -36,   1 ]
		

Links

• Peter Luschny, The Bell transform

Crossrefs

Cf. A000110, A187761, A264428, A264429.

Programs

Sage

# uses[bell_transform from A264428, inverse_bell_transform from A264429]
def A264431_matrix(dim):
    uno = [1]*dim
    bell_numbers = [sum(bell_transform(n, uno)) for n in range(dim)]
    bell_number_2 = [sum(bell_transform(n, bell_numbers)) for n in range(dim)]
    return inverse_bell_transform(dim, bell_number_2)
A264431_matrix(10)