OFFSET
1,2
COMMENTS
LINKS
Alois P. Heinz, Rows n = 1..141, flattened
FORMULA
E.g.f. for column k is x^k/k!*exp(exp(x)-1).
Sum_{k=1..n} k * T(n,k) = A070071(n). - Alois P. Heinz, Mar 03 2020
EXAMPLE
The set {1,2,3} has 5 partitions, {{1, 2, 3}}, {{2, 3}, {1}}, {{1, 3}, {2}}, {{1, 2}, {3}}, and {{2}, {3}, {1}}, and there are a total of 3 blocks of size 2, so T(3,2)=3.
Triangle begins:
1;
2, 1;
6, 3, 1;
20, 12, 4, 1;
75, 50, 20, 5, 1;
312, 225, 100, 30, 6, 1;
...
MAPLE
b:= proc(n) option remember; `if`(n=0, [1, 0],
add((p-> p+[0, p[1]*x^j])(b(n-j)*
binomial(n-1, j-1)), j=1..n))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=1..n))(b(n)[2]):
seq(T(n), n=1..12); # Alois P. Heinz, Apr 24 2017
MATHEMATICA
Table[Table[Length[Select[Level[SetPartitions[m], {2}], Length[#]==n&]], {n, 1, m}], {m, 1, 10}]//Grid
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Dec 04 2010
STATUS
approved