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A241633 Number of compositions of n with exactly eight descents.

%I A241633 #8 Nov 28 2023 09:15:21
%S A241633 34,474,3914,24222,123713,548540,2178219,7909965,26662725,84357961,
%T A241633 252677505,721404913,1974020281,5200561960,13240895310,32684520969,
%U A241633 78435463950,183422986603,418849888662,935640152746,2047838246581,4397763452093,9278220501698
%N A241633 Number of compositions of n with exactly eight descents.
%H A241633 Joerg Arndt and Alois P. Heinz, <a href="/A241633/b241633.txt">Table of n, a(n) for n = 24..1000</a>
%p A241633 b:= proc(n, i) option remember;
%p A241633       `if`(n=0, 1, convert(series(add(b(n-j, j)*
%p A241633       `if`(j<i, x, 1), j=1..n), x, 9), polynom))
%p A241633     end:
%p A241633 a:= n-> coeff(b(n, 0), x, 8):
%p A241633 seq(a(n), n=24..50);
%t A241633 b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[b[n - j, j]*
%t A241633    If[j < i, x, 1], {j, 1, n}] // Expand];
%t A241633 a[n_] := Coefficient[b[n, 0], x, 8];
%t A241633 Table[a[n], {n, 24, 50}] (* _Jean-François Alcover_, Nov 28 2023, from Maple code *)
%Y A241633 Column k=8 of A238343 and of A238344.
%K A241633 nonn
%O A241633 24,1
%A A241633 _Joerg Arndt_ and _Alois P. Heinz_, Apr 26 2014