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%I #8 Nov 28 2023 10:48:16
%S 89,1529,15072,109700,651755,3333143,15159290,62673818,239267852,
%T 853417204,2869778022,9163554647,27947044811,81799126374,230699706092,
%U 629085587197,1663426352840,4275866388599,10708451601656,26178837135330,62580214195713,146503017803381
%N Number of compositions of n with exactly ten descents.
%H Joerg Arndt and Alois P. Heinz, <a href="/A241635/b241635.txt">Table of n, a(n) for n = 30..1000</a>
%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, 11), polynom))
%p end:
%p a:= n-> coeff(b(n, 0), x, 10):
%p seq(a(n), n=30..55);
%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, 10];
%t Table[a[n], {n, 30, 55}] (* _Jean-François Alcover_, Nov 28 2023, from Maple code *)
%Y Column k=10 of A238343 and of A238344.
%K nonn,changed
%O 30,1
%A _Joerg Arndt_ and _Alois P. Heinz_, Apr 26 2014
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