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Number of different coefficient values in expansion of Product_{k=1..n} (1-x^k).
1

%I #14 Feb 04 2024 13:14:36

%S 1,2,2,3,4,3,4,5,5,5,5,5,6,7,7,9,9,11,12,15,16,17,21,23,25,33,35,41,

%T 43,53,55,77,74,97,85,135,111,175,131,223,157,269,187,315,219,375,245,

%U 437,280,505,320,593,357,671,398,761,445,825,489,933,529,1039,576,1119,627,1211,682,1309,730,1415

%N Number of different coefficient values in expansion of Product_{k=1..n} (1-x^k).

%o (PARI) a(n) = #Set(Vec(prod(k=1, n, 1-x^k)));

%o (Python)

%o from collections import Counter

%o def A369879(n):

%o c = {0:1}

%o for k in range(1,n+1):

%o d = Counter(c)

%o for j in c:

%o d[j+k] -= c[j]

%o c = d

%o return len(set(c.values()))+int(max(c)+1>len(c)) # _Chai Wah Wu_, Feb 04 2024

%Y Cf. A010815, A039822, A369790.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 04 2024