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A243237 Number of isoscent sequences of length n with maximal number of ascents.

%I A243237 #10 Aug 27 2021 08:23:59
%S A243237 1,1,1,4,3,25,17,2,172,53,7,1422,436,72,5,7894,1854,271,19,86372,
%T A243237 19919,3179,312,14,527951,102503,14324,1287,56,7237537,1373018,198783,
%U A243237 20572,1350,42,48862041,8055893,1032239,96532,5866,174,801902467,129068117,16767855
%N A243237 Number of isoscent sequences of length n with maximal number of ascents.
%H A243237 Joerg Arndt and Alois P. Heinz, <a href="/A243237/b243237.txt">Table of n, a(n) for n = 0..100</a>
%F A243237 a(n) = A242351(n,n+3-ceiling(2*sqrt(n+2))).
%p A243237 b:= proc(n, i, t) option remember; `if`(n<1, 1, expand(add(
%p A243237       `if`(j>i, x, 1) *b(n-1, j, t+`if`(j=i, 1, 0)), j=0..t+1)))
%p A243237     end:
%p A243237 a:= n-> (p-> coeff(p, x, degree(p)))(b(n-1, 0$2)):
%p A243237 seq(a(n), n=0..50);
%t A243237 b[n_, i_, t_] := b[n, i, t] = If[n < 1, 1, Expand[Sum[
%t A243237     If[j > i, x, 1]*b[n - 1, j, t + If[j == i, 1, 0]], {j, 0, t + 1}]]];
%t A243237 a[n_] := With[{p = b[n - 1, 0, 0]}, Coefficient[p, x, Exponent[p, x]]];
%t A243237 Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Aug 27 2021, after Maple code *)
%K A243237 nonn
%O A243237 0,4
%A A243237 _Joerg Arndt_ and _Alois P. Heinz_, Jun 01 2014