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A318115 Number of compositions of n into exactly n nonnegative parts <= seven.

%I A318115 #12 Nov 03 2021 10:09:30
%S A318115 1,1,3,10,35,126,462,1716,6427,24229,91828,349570,1335698,5119856,
%T A318115 19678452,75814560,292695291,1132074847,4385740683,17015510820,
%U A318115 66102536360,257103599280,1001078753370,3901733646660,15220908863866,59427261280126,232201593611796
%N A318115 Number of compositions of n into exactly n nonnegative parts <= seven.
%H A318115 Alois P. Heinz, <a href="/A318115/b318115.txt">Table of n, a(n) for n = 0..1669</a>
%F A318115 a(n) = [x^n] ((x^8-1)/(x-1))^n.
%F A318115 a(n) <= A088218(n) with equality only for n < 8.
%F A318115 a(n) = Sum_{k=0..floor(n/8)} (-1)^k * binomial(n,k) * binomial(2*n-8*k-1,n-8*k). - _Ilya Gutkovskiy_, Nov 03 2021
%p A318115 b:= proc(n, i) option remember; `if`(n=0, 1,
%p A318115       `if`(i=0, 0, add(b(n-j, i-1), j=0..min(n, 7))))
%p A318115     end:
%p A318115 a:= n-> b(n$2):
%p A318115 seq(a(n), n=0..30);
%Y A318115 Column k=7 of A305161.
%Y A318115 Cf. A088218.
%K A318115 nonn
%O A318115 0,3
%A A318115 _Alois P. Heinz_, Aug 17 2018