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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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 LINKS Peter Luschny, The Bell transform 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) # The function bell_transform is defined in 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 Cf. A000110, A264428. Sequence in context: A091925 A034370 A144402 * A324163 A127537 A265314 Adjacent sequences:  A264426 A264427 A264428 * A264430 A264431 A264432 KEYWORD sign,tabl AUTHOR Peter Luschny, Nov 13 2015 STATUS approved

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Last modified February 24 10:27 EST 2020. Contains 332209 sequences. (Running on oeis4.)