A264435 Triangle read by rows, Bell transform of the complementary Bell numbers (A000587).

1, 0, 1, 0, -1, 1, 0, 0, -3, 1, 0, 1, 3, -6, 1, 0, 1, 5, 15, -10, 1, 0, -2, -9, 0, 45, -15, 1, 0, -9, -35, -84, -70, 105, -21, 1, 0, -9, 19, -14, -259, -350, 210, -28, 1, 0, 50, 369, 873, 966, -189, -1134, 378, -36, 1, 0, 267, 611, 1260, 3645, 5565, 1827, -2940, 630, -45, 1

Offset: 0

Author

Peter Luschny, Dec 01 2015

Keywords

• sign
• tabl

Examples

			Triangle starts:
[1]
[0,   1]
[0,  -1,   1]
[0,   0,  -3,    1]
[0,   1,   3,   -6,    1]
[0,   1,   5,   15,  -10,    1]
[0,  -2,  -9,    0,   45,  -15,     1]
[0,  -9, -35,  -84,  -70,  105,   -21,     1]
[0,  -9,  19,  -14, -259, -350,   210,   -28,  1]
[0,  50, 369,  873,  966, -189, -1134,   378, -36,   1]
[0, 267, 611, 1260, 3645, 5565,  1827, -2940, 630, -45, 1]
		

Links

• Peter Luschny, The Bell transform

Crossrefs

Cf. A000587, A264428.

Programs

Sage

# uses[bell_transform from A264428]
def A264435_triangle(dim):
    uno = [1]*dim
    complementary_bell_numbers = [sum((-1)^n*b for (n,b) in enumerate (bell_transform(n,uno))) for n in range(dim)]
    for n in range(dim):
        print(bell_transform(n, complementary_bell_numbers))
A264435_triangle(12)