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A332716 Number of compositions of n^2 where each part is less than or equal to n.

%I A332716 #18 Oct 31 2022 06:26:29
%S A332716 1,1,5,149,20569,11749641,26649774581,236837126431501,
%T A332716 8237168505776637425,1125036467745713090813969,
%U A332716 606147434557459526483161067501,1293596348252277644272081532560154645,10970544241076481629439275072320816659677161
%N A332716 Number of compositions of n^2 where each part is less than or equal to n.
%C A332716 All terms are odd.
%H A332716 Alois P. Heinz, <a href="/A332716/b332716.txt">Table of n, a(n) for n = 0..57</a>
%F A332716 a(n) = Sum_{i=0..n-1} A048004(n^2-1,i) for i > 0.
%e A332716 a(2) = 5: 22, 211, 121, 112, 1111.
%p A332716 b:= proc(n, k) option remember; `if`(n=0, 1,
%p A332716       add(b(n-d, k), d=1..min(n, k)))
%p A332716     end:
%p A332716 a:= n-> b(n^2, n):
%p A332716 seq(a(n), n=0..15);
%t A332716 b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - d, k], {d, 1, Min[n, k]}]];
%t A332716 a[n_] := b[n^2, n];
%t A332716 Table[a[n], {n, 0, 15}] (* _Jean-François Alcover_, Oct 31 2022, after _Alois P. Heinz_ *)
%Y A332716 Cf. A000079, A000290, A008464, A048004, A090667, A103488, A332721, A332796.
%K A332716 nonn
%O A332716 0,3
%A A332716 _Alois P. Heinz_, Feb 20 2020