cp's OEIS Frontend

A318117 Number of compositions of n into exactly n nonnegative parts <= ten.

%I A318117 #12 Nov 03 2021 20:58:57
%S A318117 1,1,3,10,35,126,462,1716,6435,24310,92378,352705,1351934,5199117,
%T A318117 20050460,77512860,300292131,1165534689,4531337778,17642948675,
%U A318117 68785126410,268497991905,1049210943531,4104103226699,16068342973950,62963565243876,246913415221671
%N A318117 Number of compositions of n into exactly n nonnegative parts <= ten.
%H A318117 Alois P. Heinz, <a href="/A318117/b318117.txt">Table of n, a(n) for n = 0..1665</a>
%F A318117 a(n) = [x^n] ((x^11-1)/(x-1))^n.
%F A318117 a(n) <= A088218(n) with equality only for n < 11.
%F A318117 a(n) = Sum_{k=0..floor(n/11)} (-1)^k * binomial(n,k) * binomial(2*n-11*k-1,n-11*k). - _Ilya Gutkovskiy_, Nov 03 2021
%p A318117 b:= proc(n, i) option remember; `if`(n=0, 1,
%p A318117       `if`(i=0, 0, add(b(n-j, i-1), j=0..min(n, 10))))
%p A318117     end:
%p A318117 a:= n-> b(n$2):
%p A318117 seq(a(n), n=0..30);
%Y A318117 Column k=10 of A305161.
%Y A318117 Cf. A088218.
%K A318117 nonn
%O A318117 0,3
%A A318117 _Alois P. Heinz_, Aug 17 2018