

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.


2



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
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OFFSET

0,9


COMMENTS

Row sums give A000142.
Row lengths are given by A000217 for n>=1.  Omar E. Pol, Oct 25 2015


LINKS

Alois P. Heinz, Rows n = 0..15, flattened
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, i) option remember; `if`(s={}, 1, expand(
add(b(s minus {j}, j)*`if`(j<i, x^i, 1), j=s)))
end:
T:= n>(p>seq(coeff(p, x, i), i=0..degree(p)))(b({$1..n}, 0)):
seq(T(n), n=0..9); # Alois P. Heinz, Oct 25 2015


CROSSREFS

Cf. A000142, A263756.
Sequence in context: A200472 A309887 A317595 * A303877 A112743 A230427
Adjacent sequences: A263750 A263751 A263752 * A263754 A263755 A263756


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



