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A332796 Number of compositions of n^2 into parts >= n.

%I A332796 #23 Mar 04 2022 11:01:49
%S A332796 1,1,2,6,26,140,882,6349,51284,457704,4459940,47019819,532485538,
%T A332796 6438774524,82710138994,1123798871990,16090426592488,241979954659728,
%U A332796 3811335657375786,62712512310820402,1075527196672980525,19186234784992217621,355349469934379290700
%N A332796 Number of compositions of n^2 into parts >= n.
%H A332796 Alois P. Heinz, <a href="/A332796/b332796.txt">Table of n, a(n) for n = 0..170</a>
%e A332796 a(0) = 1: (), the empty composition.
%e A332796 a(1) = 1: 1.
%e A332796 a(2) = 2: 22, 4.
%e A332796 a(3) = 6: 333, 36, 63, 45, 54, 9.
%e A332796 a(4) = 26: 4444, 556, 565, 655, 466, 646, 664, 457, 475, 547, 574, 745, 754, 448, 484, 844, 88, 79, 97, 6(10), (10)6, 5(11), (11)5, 4(12), (12)4, (16).
%p A332796 b:= proc(n, k) option remember; `if`(n=0, 1,
%p A332796       add(b(n-j, k), j=k..n))
%p A332796     end:
%p A332796 a:= n-> b(n^2, n):
%p A332796 seq(a(n), n=0..23);
%t A332796 b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - j, k], {j, k, n}]];
%t A332796 a[n_] := b[n^2, n];
%t A332796 Table[a[n], {n, 0, 23}] (* _Jean-François Alcover_, Mar 04 2022, after _Alois P. Heinz_ *)
%Y A332796 Cf. A011782, A103488, A332716, A332721, A332747.
%K A332796 nonn
%O A332796 0,3
%A A332796 _Alois P. Heinz_, Feb 24 2020