OFFSET
0,6
COMMENTS
Row sums give A000142.
LINKS
Alois P. Heinz, Rows n = 0..23, flattened
FindStat - Combinatorial Statistic Finder, The sum of the descent bottoms of a permutations.
EXAMPLE
Triangle begins:
1;
1;
1,1;
1,3,1,1;
1,7,3,8,3,1,1;
1,15,7,34,18,14,18,8,3,1,1;
1,31,15,122,72,69,147,83,71,33,45,18,8,3,1,1;
...
MAPLE
b:= proc(s) option remember; (n-> `if`(n=0, 1, expand(
add(b(s minus {j})*`if`(j<n, x^j, 1), j=s))))(nops(s))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b({$1..n})):
seq(T(n), n=0..9); # Alois P. Heinz, Oct 25 2015, revised, Jan 31 2023
MATHEMATICA
b[s_] := b[s] = With[{n = Length[s]}, If[n == 0, 1, Expand[ Sum[b[s~Complement~{j}]*If[j < n, x^j, 1], {j, s}]]]];
T[n_] := CoefficientList[b[Range[n]], x];
Table[T[n], {n, 0, 9}] // Flatten (* Jean-François Alcover, May 26 2023, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Christian Stump, Oct 19 2015
EXTENSIONS
Two terms (for rows 0 and 1) prepended and more terms from Alois P. Heinz, Oct 25 2015
STATUS
approved