A369791 - OEIS

%I #15 Feb 03 2024 10:15:32

%S 1,1,1,3,8,22,70,262,1088,5076,26490,146542,896402,5662622,39826304,

%T 279072864,2232912264,17866212198,153323343990,1379920982310,

%U 13115759159982,131158174385100

%N 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 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 (Python)

%o from itertools import islice

%o from collections import Counter

%o def A369791_gen(): # generator of terms

%o     c, a = {0:1}, []

%o     while True:

%o         a.append(max(c.values()))

%o         yield a[-1]

%o         d = Counter(c)

%o         for k in c:

%o             for b in a:

%o                 d[k+b] += c[k]

%o         c = d

%o A369791_list = list(islice(A369791_gen(),10)) # _Chai Wah Wu_, Feb 01 2024

%Y Cf. A000140.

%K nonn,more

%O 0,4

%A _Ilya Gutkovskiy_, Feb 01 2024

%E a(16)-a(20) from _Alois P. Heinz_, Feb 01 2024

%E a(21) from _Chai Wah Wu_, Feb 01 2024