A264434 Triangle read by rows, inverse 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, 1, -3, 1, 0, -1, 7, -6, 1, 0, 1, -15, 25, -10, 1, 0, 0, 31, -90, 65, -15, 1, 0, -7, -56, 301, -350, 140, -21, 1, 0, 33, 35, -938, 1701, -1050, 266, -28, 1, 0, -102, 423, 2485, -7686, 6951, -2646, 462, -36, 1, 0, 240, -3219, -3450, 31885

Offset: 0

Author

Peter Luschny, Dec 02 2015

Keywords

• sign
• tabl

Examples

			[ 1]
[ 0,     1]
[ 0,    -1,     1]
[ 0,     1,    -3,     1]
[ 0,    -1,     7,    -6,      1]
[ 0,     1,   -15,    25,    -10,     1]
[ 0,     0,    31,   -90,     65,    -15,    1]
[ 0,    -7,   -56,   301,   -350,    140,   -21,  1]
[ 0,    33,    35,  -938,   1701,  -1050,   266, -28,  1]
[ 0,  -102,   423,  2485,  -7686,   6951, -2646, 462, -36, 1]
		

Crossrefs

Cf. A048993, A264428, A264429, A264431.

Programs

Sage

# uses[bell_transform from A264428, inverse_bell_transform from A264429]
def A264434_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)]
    bell_number_3 = [sum(bell_transform(n, bell_number_2)) for n in range(dim)]
    return inverse_bell_transform(dim, bell_number_3)
A264434_matrix(10)