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A224652 Triangle read by rows: T(n,k) is the number of permutations of n elements with k the (smallest) header (first element) of the longest descending subsequence.

%I A224652 #16 Feb 03 2017 17:13:32
%S A224652 1,1,1,1,2,3,1,5,8,10,1,14,25,35,45,1,42,89,141,196,251,1,132,357,644,
%T A224652 966,1302,1638,1,429,1602,3284,5300,7526,9878,12300,1,1430,7959,18423,
%U A224652 31947,47859,65619,84765,104877,1,4862,43127,112255,209500,331795,475738,637657,813730,1000135
%N A224652 Triangle read by rows: T(n,k) is the number of permutations of n elements with k the (smallest) header (first element) of the longest descending subsequence.
%C A224652 Table II "Distribution of F_n" on p. 99 of the Pilpel reference.
%C A224652 Column 2 is A000108; column 3 is A006219; the diagonal is A006220; the row sums are A000142.
%H A224652 Sean A. Irvine, <a href="/A224652/b224652.txt">Table of n, a(n) for n = 1..91</a>
%H A224652 S. Pilpel, <a href="http://dx.doi.org/10.1016/0097-3165(90)90022-O">Descending subsequences of random permutations</a>, J. Combin. Theory, A 53 (1990), 96-116.
%e A224652 Triangle begins
%e A224652 1;
%e A224652 1, 1;
%e A224652 1, 2, 3;
%e A224652 1, 5, 8, 10;
%e A224652 1, 14, 25, 35, 45;
%e A224652 1, 42, 89, 141, 196, 251;
%e A224652 1, 132, 357, 644, 966, 1302, 1638;
%e A224652 1, 429, 1602, 3284, 5300, 7526, 9878, 12300;
%e A224652 1, 1430, 7959, 18423, 31947, 47859, 65619, 84765, 104877;
%e A224652 1, 4862, 43127, 112255, 209500, 331795, 475738, 637657, 813730, 1000135;
%e A224652 ...
%Y A224652 Cf. A000108, A006219, A006220, A000142 (row sums).
%Y A224652 Cf. A047874 (Table I, "Distribution of L_n" on p. 99 of the Pilpel reference).
%K A224652 nonn,tabl
%O A224652 1,5
%A A224652 _Joerg Arndt_, Apr 13 2013