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A243231 Number of isoscent sequences of length n with exactly five ascents.

%I A243231 #9 Aug 27 2021 08:52:55
%S A243231 53,2751,56905,771451,8134377,72508373,573143602,4140884203,
%T A243231 27910175578,178061795837,1086790574778,6397136152382,36542124316824,
%U A243231 203563522508400,1110216333288652,5946996009211010,31369110229193995,163289639236069520,840329677373681576
%N A243231 Number of isoscent sequences of length n with exactly five ascents.
%H A243231 Joerg Arndt and Alois P. Heinz, <a href="/A243231/b243231.txt">Table of n, a(n) for n = 9..100</a>
%p A243231 b:= proc(n, i, t) option remember; `if`(n<1, 1, expand(add(
%p A243231       `if`(j>i, x, 1) *b(n-1, j, t+`if`(j=i, 1, 0)), j=0..t+1)))
%p A243231     end:
%p A243231 a:= n-> coeff(b(n-1, 0$2), x, 5):
%p A243231 seq(a(n), n=9..35);
%t A243231 b[n_, i_, t_] := b[n, i, t] = If[n < 1, 1, Expand[Sum[
%t A243231     If[j > i, x, 1] *b[n - 1, j, t + If[j == i, 1, 0]], {j, 0, t + 1}]]];
%t A243231 a[n_] := Coefficient[b[n - 1, 0, 0], x, 5];
%t A243231 Table[a[n], {n, 9, 35}] (* _Jean-François Alcover_, Aug 27 2021, after Maple code *)
%Y A243231 Column k=5 of A242351.
%K A243231 nonn
%O A243231 9,1
%A A243231 _Joerg Arndt_ and _Alois P. Heinz_, Jun 01 2014