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A369791 a(n) is the maximal coefficient of (1 + x^a(1)) * (1 + x^a(1) + x^a(2)) * ... * (1 + x^a(1) + x^a(2) + ... + x^a(n-1)).

%I A369791 #15 Feb 03 2024 10:15:32
%S A369791 1,1,1,3,8,22,70,262,1088,5076,26490,146542,896402,5662622,39826304,
%T A369791 279072864,2232912264,17866212198,153323343990,1379920982310,
%U A369791 13115759159982,131158174385100
%N A369791 a(n) is the maximal coefficient of (1 + x^a(1)) * (1 + x^a(1) + x^a(2)) * ... * (1 + x^a(1) + x^a(2) + ... + x^a(n-1)).
%t A369791 a[n_] := a[n] = Max[CoefficientList[Product[(1 + Sum[x^a[j], {j, 1, i}]), {i, 1, n - 1}], x]]; Table[a[n], {n, 0, 15}]
%o A369791 (Python)
%o A369791 from itertools import islice
%o A369791 from collections import Counter
%o A369791 def A369791_gen(): # generator of terms
%o A369791     c, a = {0:1}, []
%o A369791     while True:
%o A369791         a.append(max(c.values()))
%o A369791         yield a[-1]
%o A369791         d = Counter(c)
%o A369791         for k in c:
%o A369791             for b in a:
%o A369791                 d[k+b] += c[k]
%o A369791         c = d
%o A369791 A369791_list = list(islice(A369791_gen(),10)) # _Chai Wah Wu_, Feb 01 2024
%Y A369791 Cf. A000140.
%K A369791 nonn,more
%O A369791 0,4
%A A369791 _Ilya Gutkovskiy_, Feb 01 2024
%E A369791 a(16)-a(20) from _Alois P. Heinz_, Feb 01 2024
%E A369791 a(21) from _Chai Wah Wu_, Feb 01 2024