A241881 - OEIS

%I #16 Feb 13 2015 04:48:10

%S 1,1,2,1,7,4,1,48,26,8,1,594,262,76,13,1,10030,3571,933,169,19,1,

%T 205271,61206,14351,2550,323,26,1,4910802,1263620,267378,45321,5918,

%U 559,34,1,134636523,30534920,5873492,939681,121689,12257,901,43,1,4166817191

%N Number of ascent sequences of length n with the maximal number of descents.

%C a(n*(n+1)/2) = a(A000217(n)) = 1.

%H Joerg Arndt and Alois P. Heinz, <a href="/A241881/b241881.txt">Table of n, a(n) for n = 0..140</a>

%F a(n) = A238858(n,Re(n-floor((sqrt(8*n-7)+1)/2))).

%p b:= proc(n, i, t) option remember; `if`(n=0, 1, expand(add(

%p       `if`(j<i, x, 1) *b(n-1, j, t+`if`(j>i, 1, 0)), j=0..t+1)))

%p     end:

%p a:= n-> (p-> coeff(p, x, degree(p)))(b(n, -1$2)):

%p seq(a(n), n=0..40);

%t b[n_, i_, t_] := b[n, i, t] = If[n == 0, 1, Expand[Sum[If[j<i, x, 1] *b[n-1, j, t + If[j>i, 1, 0]], {j, 0, t+1}]]]; a[n_] := Function[{p}, Coefficient[p, x, Exponent[ p, x ]]][b[n, -1, -1]]; Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Feb 13 2015, after Maple *)

%K nonn

%O 0,3

%A _Joerg Arndt_ and _Alois P. Heinz_, May 01 2014