A241632 - OEIS

%I #10 Nov 28 2023 09:15:16

%S 21,259,1932,10898,51083,208936,768594,2594957,8158005,24140097,

%T 67794864,181889780,468678716,1164905882,2803070038,6549961919,

%U 14901997455,33085162997,71822232573,152710556875,318509850193,652536555773,1314728710475,2607856668543

%N Number of compositions of n with exactly seven descents.

%H Joerg Arndt and Alois P. Heinz, <a href="/A241632/b241632.txt">Table of n, a(n) for n = 21..1000</a>

%e a(21) = 21: [3,2,1,2,1,3,2,1,3,2,1], [3,2,1,3,2,1,2,1,3,2,1], [3,2,1,3,2,1,3,2,1,2,1], [2,1,3,2,1,3,2,1,3,2,1], [2,1,2,1,2,1,3,2,1,3,2,1], [3,2,1,3,2,1,2,1,2,1,2,1], [2,1,2,1,3,2,1,2,1,3,2,1], [2,1,3,2,1,2,1,3,2,1,2,1], [3,2,1,2,1,3,2,1,2,1,2,1], [3,2,1,2,1,2,1,2,1,3,2,1], [2,1,3,2,1,2,1,2,1,3,2,1], [3,2,1,2,1,2,1,3,2,1,2,1], [2,1,2,1,3,2,1,3,2,1,2,1], [2,1,3,2,1,3,2,1,2,1,2,1], [3,2,1,2,1,2,1,2,1,2,1,2,1], [2,1,2,1,2,1,2,1,2,1,3,2,1], [2,1,3,2,1,2,1,2,1,2,1,2,1], [2,1,2,1,2,1,2,1,3,2,1,2,1], [2,1,2,1,2,1,3,2,1,2,1,2,1], [2,1,2,1,3,2,1,2,1,2,1,2,1], [2,1,2,1,2,1,2,1,2,1,2,1,2,1].

%p b:= proc(n, i) option remember;

%p       `if`(n=0, 1, convert(series(add(b(n-j, j)*

%p       `if`(j<i, x, 1), j=1..n), x, 8), polynom))

%p     end:

%p a:= n-> coeff(b(n, 0), x, 7):

%p seq(a(n), n=21..50);

%t b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[b[n - j, j]*

%t    If[j < i, x, 1], {j, 1, n}] // Expand];

%t a[n_] := Coefficient[b[n, 0], x, 7];

%t Table[a[n], {n, 21, 50}] (* _Jean-François Alcover_, Nov 28 2023, from Maple code *)

%Y Column k=7 of A238343 and of A238344.

%K nonn

%O 21,1

%A _Joerg Arndt_ and _Alois P. Heinz_, Apr 26 2014