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A264429
Triangle read by rows, inverse Bell transform of Bell numbers.
9
1, 0, 1, 0, -1, 1, 0, 1, -3, 1, 0, 0, 7, -6, 1, 0, -5, -10, 25, -10, 1, 0, 18, -20, -75, 65, -15, 1, 0, -7, 231, 70, -315, 140, -21, 1, 0, -338, -840, 1064, 945, -980, 266, -28, 1, 0, 2215, -1278, -8918, 1512, 4935, -2520, 462, -36, 1
OFFSET
0,9
EXAMPLE
[ 1 ]
[ 0, 1 ]
[ 0, -1, 1 ]
[ 0, 1, -3, 1 ]
[ 0, 0, 7, -6, 1 ]
[ 0, -5, -10, 25, -10, 1 ]
[ 0, 18, -20, -75, 65, -15, 1 ]
[ 0, -7, 231, 70, -315, 140, -21, 1 ]
[ 0, -338, -840, 1064, 945, -980, 266, -28, 1 ]
[ 0, 2215, -1278, -8918, 1512, 4935, -2520, 462, -36, 1 ]
MATHEMATICA
rows = 10;
M = Table[BellY[n, k, BellB[Range[0, rows-1]]], {n, 0, rows-1}, {k, 0, rows-1}] // Inverse;
A264429 = Table[M[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 22 2018 *)
PROG
(Sage) # uses[bell_transform from A264428]
def inverse_bell_transform(dim, L):
M = matrix(ZZ, dim)
for n in range(dim):
row = bell_transform(n, L)
for k in (0..n): M[n, k] = row[k]
return M.inverse()
def A264429_matrix(dim):
uno = [1]*dim
bell_numbers = [sum(bell_transform(n, uno)) for n in range(dim)]
return inverse_bell_transform(dim, bell_numbers)
A264429_matrix(10)
CROSSREFS
Sequence in context: A369199 A034370 A144402 * A324163 A127537 A265314
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Nov 13 2015
STATUS
approved