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A265313
Square array read by ascending antidiagonals, complementary Bell numbers iterated by the Bell transform.
1
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
0,13
EXAMPLE
[ 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
PROG
(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))
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Dec 06 2015
STATUS
approved