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A263753
Triangle read by rows: T(n,k) (n>=0, k>=0) is the number of permutations of n with sum of descent tops equal to k.
3
1, 1, 1, 0, 1, 1, 0, 1, 3, 0, 1, 1, 0, 1, 3, 7, 1, 3, 7, 0, 1, 1, 0, 1, 3, 7, 16, 3, 14, 17, 32, 3, 7, 15, 0, 1, 1, 0, 1, 3, 7, 16, 34, 14, 32, 69, 72, 129, 32, 68, 70, 118, 7, 15, 31, 0, 1, 1, 0, 1, 3, 7, 16, 34, 77, 32, 100, 149, 274, 292, 496, 220, 388, 536
OFFSET
0,9
COMMENTS
Row sums give A000142.
Row lengths are given by A000217 for n>=1. - Omar E. Pol, Oct 25 2015
LINKS
FindStat - Combinatorial Statistic Finder, The sum of the descent tops of a permutation
EXAMPLE
Triangle begins:
1;
1;
1,0,1;
1,0,1,3,0,1;
1,0,1,3,7,1,3,7,0,1;
1,0,1,3,7,16,3,14,17,32,3,7,15,0,1;
1,0,1,3,7,16,34,14,32,69,72,129,32,68,70,118,7,15,31,0,1;
...
MAPLE
b:= proc(s) option remember; (n-> `if`(n=0, 1, expand(
add(b(s minus {j})*`if`(j<n, x^n, 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
CROSSREFS
Sequence in context: A200472 A309887 A317595 * A303877 A112743 A230427
KEYWORD
nonn,tabf
AUTHOR
Christian Stump, Oct 19 2015
EXTENSIONS
One term prepended and one term corrected by Alois P. Heinz, Oct 25 2015
STATUS
approved