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A241632 Number of compositions of n with exactly seven descents.

%I A241632 #10 Nov 28 2023 09:15:16
%S A241632 21,259,1932,10898,51083,208936,768594,2594957,8158005,24140097,
%T A241632 67794864,181889780,468678716,1164905882,2803070038,6549961919,
%U A241632 14901997455,33085162997,71822232573,152710556875,318509850193,652536555773,1314728710475,2607856668543
%N A241632 Number of compositions of n with exactly seven descents.
%H A241632 Joerg Arndt and Alois P. Heinz, <a href="/A241632/b241632.txt">Table of n, a(n) for n = 21..1000</a>
%e A241632 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 A241632 b:= proc(n, i) option remember;
%p A241632       `if`(n=0, 1, convert(series(add(b(n-j, j)*
%p A241632       `if`(j<i, x, 1), j=1..n), x, 8), polynom))
%p A241632     end:
%p A241632 a:= n-> coeff(b(n, 0), x, 7):
%p A241632 seq(a(n), n=21..50);
%t A241632 b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[b[n - j, j]*
%t A241632    If[j < i, x, 1], {j, 1, n}] // Expand];
%t A241632 a[n_] := Coefficient[b[n, 0], x, 7];
%t A241632 Table[a[n], {n, 21, 50}] (* _Jean-François Alcover_, Nov 28 2023, from Maple code *)
%Y A241632 Column k=7 of A238343 and of A238344.
%K A241632 nonn
%O A241632 21,1
%A A241632 _Joerg Arndt_ and _Alois P. Heinz_, Apr 26 2014