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A241634 Number of compositions of n with exactly nine descents.

%I A241634 #8 Nov 28 2023 10:47:53
%S A241634 55,856,7752,52203,288439,1377331,5868260,22792116,81944050,275852636,
%T A241634 877202199,2653544633,7679263550,21360356057,57331068005,148970797526,
%U A241634 375812977280,922708833921,2209559805490,5170203452802,11840994145688,26581854857244,58569145064714
%N A241634 Number of compositions of n with exactly nine descents.
%H A241634 Joerg Arndt and Alois P. Heinz, <a href="/A241634/b241634.txt">Table of n, a(n) for n = 27..1000</a>
%p A241634 b:= proc(n, i) option remember;
%p A241634       `if`(n=0, 1, convert(series(add(b(n-j, j)*
%p A241634       `if`(j<i, x, 1), j=1..n), x, 10), polynom))
%p A241634     end:
%p A241634 a:= n-> coeff(b(n, 0), x, 9):
%p A241634 seq(a(n), n=27..50);
%t A241634 b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[b[n - j, j]*
%t A241634    If[j < i, x, 1], {j, 1, n}] // Expand];
%t A241634 a[n_] := Coefficient[b[n, 0], x, 9];
%t A241634 Table[a[n], {n, 27, 50}] (* _Jean-François Alcover_, Nov 28 2023, from Maple code *)
%Y A241634 Column k=9 of A238343 and of A238344.
%K A241634 nonn
%O A241634 27,1
%A A241634 _Joerg Arndt_ and _Alois P. Heinz_, Apr 26 2014