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 A106436 Difference array of Bell numbers A000110 read by antidiagonals. 14
 1, 0, 1, 1, 1, 2, 1, 2, 3, 5, 4, 5, 7, 10, 15, 11, 15, 20, 27, 37, 52, 41, 52, 67, 87, 114, 151, 203, 162, 203, 255, 322, 409, 523, 674, 877, 715, 877, 1080, 1335, 1657, 2066, 2589, 3263, 4140, 3425, 4140, 5017, 6097, 7432, 9089, 11155, 13744, 17007, 21147 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Essentially Aitken's array A011971 with first column A000296. Mirror image of A182930. - Alois P. Heinz, Jan 29 2019 LINKS Alois P. Heinz, Rows n = 0..140, flattened Jocelyn Quaintance and Harris Kwong, A combinatorial interpretation of the Catalan and Bell number difference tables, Integers, 13 (2013), #A29. FORMULA Double-exponential generating function: sum_{n, k} a(n-k, k) x^n/n! y^k/k! = exp(exp{x+y}-1-x). a(n,k) = Sum_{i=k..n} (-1)^(n-i)*binomial(n-k,i-k)*Bell(i). - Vladeta Jovovic, Oct 14 2006 EXAMPLE 1;    0,  1;    1,  1,  2;    1,  2,  3,  5;    4,  5,  7, 10, 15;   11, 15, 20, 27, 37, 52;   ... MAPLE b:= proc(n) option remember; `if`(n=0, 1, add(       b(n-j)*binomial(n-1, j-1), j=1..n))     end: T:= proc(n, k) option remember; `if`(k=0, b(n),       T(n+1, k-1)-T(n, k-1))     end: seq(seq(T(n, d-n), n=0..d), d=0..12);  # Alois P. Heinz, Jan 29 2019 MATHEMATICA bb = Array[BellB, m = 12, 0]; dd[n_] := Differences[bb, n]; A = Array[dd, m, 0]; Table[A[[n-k+1, k+1]], {n, 0, m-1}, {k, 0, n}] // Flatten (* Jean-François Alcover, May 26 2019 *) CROSSREFS Cf. A000110, A182930. Diagonals give A005493, A011965-A011967, A191099, A000298, A011968-A011970. T(2n,n) gives A020556. Sequence in context: A274491 A076492 A127462 * A075758 A125596 A253026 Adjacent sequences:  A106433 A106434 A106435 * A106437 A106438 A106439 KEYWORD nonn,easy,tabl AUTHOR Philippe Deléham, May 29 2005 STATUS approved

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Last modified July 29 17:41 EDT 2021. Contains 346346 sequences. (Running on oeis4.)