OFFSET
0,6
COMMENTS
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
KEYWORD
AUTHOR
Philippe Deléham, May 29 2005
STATUS
approved