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A318113 Number of compositions of n into exactly n nonnegative parts <= five.

%I A318113 #13 Nov 03 2021 10:06:59
%S A318113 1,1,3,10,35,126,456,1667,6147,22825,85228,319683,1203632,4546270,
%T A318113 17218995,65372310,248705155,947926359,3618884895,13836004764,
%U A318113 52968655260,203022926480,779008308235,2992051471500,11502445734096,44256184906376,170408995261326
%N A318113 Number of compositions of n into exactly n nonnegative parts <= five.
%H A318113 Alois P. Heinz, <a href="/A318113/b318113.txt">Table of n, a(n) for n = 0..1687</a>
%F A318113 a(n) = [x^n] ((x^6-1)/(x-1))^n.
%F A318113 a(n) <= A088218(n) with equality only for n < 6.
%F A318113 a(n) = Sum_{k=0..floor(n/6)} (-1)^k * binomial(n,k) * binomial(2*n-6*k-1,n-6*k). - _Ilya Gutkovskiy_, Nov 03 2021
%p A318113 b:= proc(n, i) option remember; `if`(n=0, 1,
%p A318113       `if`(i=0, 0, add(b(n-j, i-1), j=0..min(n, 5))))
%p A318113     end:
%p A318113 a:= n-> b(n$2):
%p A318113 seq(a(n), n=0..30);
%Y A318113 Column k=5 of A305161.
%Y A318113 Cf. A088218.
%K A318113 nonn
%O A318113 0,3
%A A318113 _Alois P. Heinz_, Aug 17 2018