A265313 Square array read by ascending antidiagonals, complementary Bell numbers iterated by the Bell transform.

1, 1, 1, 1, -1, 1, 1, -1, 0, 1, 1, -1, 2, 1, 1, 1, -1, 2, -4, 1, 1, 1, -1, 2, -6, 9, -2, 1, 1, -1, 2, -6, 22, -22, -9, 1, 1, -1, 2, -6, 24, -95, 54, -9, 1, 1, -1, 2, -6, 24, -118, 472, -139, 50, 1, 1, -1, 2, -6, 24, -120, 683, -2638, 372, 267, 1, 1, -1, 2, -6, 24

Offset: 0

Author

Peter Luschny, Dec 06 2015

Keywords

• sign
• tabl

Examples

			[ 1,  1, 1,  1,  1,   1,    1,     1,     1, ...] A000012
[ 1, -1, 0,  1,  1,  -2,   -9,    -9,    50, ...] A000587
[ 1, -1, 2, -4,  9, -22,   54,  -139,   372, ...] A265023
[ 1, -1, 2, -6, 22, -95,  472, -2638, 16343, ...]
[ 1, -1, 2, -6, 24, -118, 683, -4533, 33862, ...]
[ 1, -1, 2, -6, 24, -120, 718, -4989, 39405, ...]
[...                                         ...]
[ 1, -1, 2, -6, 24, -120, 720, -5040, 40320, ...] A133942
		

Links

• Peter Luschny, The Bell transform

Crossrefs

Cf. A000012, A000587, A133942, A264428, A265023, A265312.

Programs

Sage

# uses[bell_transform from A264428]
def complementary_bell_number_matrix(ord, len):
    b = [1]*len; L = [b]
    for k in (1..ord-1):
        b = [sum((-1)^n*c for (n, c) in enumerate(bell_transform(n, b))) for n in range(len)]
        L.append(b)
    return matrix(ZZ, L)
print(complementary_bell_number_matrix(6,9))