OFFSET
0,3
LINKS
Alois P. Heinz, Rows n = 0..250, flattened
Wikipedia, Partition of a set
FORMULA
Sum_{k=1..n} k * T(n,k) = A288785(n).
EXAMPLE
T(4,1) = 5: 1234, 123|4, 124|3, 134|2, 1|234.
T(6,2) = 10: 123|456, 124|356, 125|346, 126|345, 134|256, 135|246, 136|245, 145|236, 146|235, 156|234.
Triangle T(n,k) begins:
1;
1;
2;
4, 1;
10, 5;
26, 26;
76, 117, 10;
232, 540, 105;
764, 2445, 931;
2620, 11338, 6909, 280;
9496, 53033, 48546, 4900;
35696, 253826, 324753, 64295;
140152, 1235115, 2131855, 691075, 15400;
...
MAPLE
b:= proc(n) option remember; expand(`if`(n=0, 1, add(
`if`(i>2, x, 1)*binomial(n-1, i-1)*b(n-i), i=1..n)))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n)):
seq(T(n), n=0..14); # Alois P. Heinz, Jun 20 2022
MATHEMATICA
b[n_] := b[n] = Expand[If[n == 0, 1, Sum[If[i > 2, x, 1]*
Binomial[n - 1, i - 1]*b[n - i], {i, 1, n}]]];
T[n_] := CoefficientList[b[n], x];
Table[T[n], {n, 0, 14}] // Flatten (* Jean-François Alcover, Jun 25 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Jun 20 2022
STATUS
approved