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A318116 Number of compositions of n into exactly n nonnegative parts <= eight.

%I A318116 #12 Nov 03 2021 10:08:42
%S A318116 1,1,3,10,35,126,462,1716,6435,24301,92278,351990,1347710,5176640,
%T A318116 19938348,76977360,297811491,1154300103,4481325903,17423296059,
%U A318116 67830758310,264387659490,1031636761290,4029420952890,15752622069630,61634789550126,241342568718696
%N A318116 Number of compositions of n into exactly n nonnegative parts <= eight.
%H A318116 Alois P. Heinz, <a href="/A318116/b318116.txt">Table of n, a(n) for n = 0..1666</a>
%F A318116 a(n) = [x^n] ((x^9-1)/(x-1))^n.
%F A318116 a(n) <= A088218(n) with equality only for n < 9.
%F A318116 a(n) = Sum_{k=0..floor(n/9)} (-1)^k * binomial(n,k) * binomial(2*n-9*k-1,n-9*k). - _Ilya Gutkovskiy_, Nov 03 2021
%p A318116 b:= proc(n, i) option remember; `if`(n=0, 1,
%p A318116       `if`(i=0, 0, add(b(n-j, i-1), j=0..min(n, 8))))
%p A318116     end:
%p A318116 a:= n-> b(n$2):
%p A318116 seq(a(n), n=0..30);
%Y A318116 Column k=8 of A305161.
%Y A318116 Cf. A088218.
%K A318116 nonn
%O A318116 0,3
%A A318116 _Alois P. Heinz_, Aug 17 2018