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A369773 Maximal coefficient of (1 + x) * (1 + x - x^2) * ... * (1 + x - x^2 + ... - (-x)^n).

%I A369773 #10 Feb 01 2024 16:11:33
%S A369773 1,1,2,3,4,6,19,59,233,1189,7046,45326,356517,3108808,30028121,
%T A369773 325635647,3830546752,49403859787,685063715374,10162709827329,
%U A369773 162776892315940,2754021620252692,49463507801582609,940216720983170113,18786988751008626812
%N A369773 Maximal coefficient of (1 + x) * (1 + x - x^2) * ... * (1 + x - x^2 + ... - (-x)^n).
%t A369773 Table[Max[CoefficientList[Product[(1 - Sum[(-x)^j, {j, 1, i}]), {i, 1, n}], x]], {n, 0, 24}]
%o A369773 (Python)
%o A369773 from collections import Counter
%o A369773 def A369773(n):
%o A369773     c = {0:1}
%o A369773     for k in range(1,n+1):
%o A369773         d = Counter(c)
%o A369773         for j in c:
%o A369773             a = c[j]
%o A369773             for i in range(1,k+1):
%o A369773                 d[j+i] += (a if i&1 else -a)
%o A369773         c = d
%o A369773     return max(c.values()) # _Chai Wah Wu_, Feb 01 2024
%Y A369773 Cf. A000140, A039828, A039909, A369705, A369774.
%K A369773 nonn
%O A369773 0,3
%A A369773 _Ilya Gutkovskiy_, Jan 31 2024