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%I #30 Jan 31 2023 15:54:08
%S 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,
%T 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,
%U 0,1,3,7,16,34,77,32,100,149,274,292,496,220,388,536
%N 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.
%C Row sums give A000142.
%C Row lengths are given by A000217 for n>=1. - _Omar E. Pol_, Oct 25 2015
%H Alois P. Heinz, <a href="/A263753/b263753.txt">Rows n = 0..23, flattened</a>
%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000111">The sum of the descent tops of a permutation</a>
%e Triangle begins:
%e 1;
%e 1;
%e 1,0,1;
%e 1,0,1,3,0,1;
%e 1,0,1,3,7,1,3,7,0,1;
%e 1,0,1,3,7,16,3,14,17,32,3,7,15,0,1;
%e 1,0,1,3,7,16,34,14,32,69,72,129,32,68,70,118,7,15,31,0,1;
%e ...
%p b:= proc(s) option remember; (n-> `if`(n=0, 1, expand(
%p add(b(s minus {j})*`if`(j<n, x^n, 1), j=s))))(nops(s))
%p end:
%p T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b({$1..n})):
%p seq(T(n), n=0..9); # _Alois P. Heinz_, Oct 25 2015, revised, Jan 31 2023
%Y Cf. A000142, A263756.
%K nonn,tabf
%O 0,9
%A _Christian Stump_, Oct 19 2015
%E One term prepended and one term corrected by _Alois P. Heinz_, Oct 25 2015
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