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A369787 Number of different coefficient values in expansion of Product_{k=1..n} (1+x^(k*(k+1)/2)).

%I A369787 #10 Feb 01 2024 19:01:49
%S A369787 1,1,2,2,3,3,4,5,6,8,13,19,28,44,71,112,168,249,321,419,549,652,797,
%T A369787 939,1104,1265,1440,1638,1842,2059,2295,2538,2809,3087,3385,3698,4032,
%U A369787 4381,4754,5143,5554,5985,6437,6910,7405,7922,8463,9027,9615,10227,10865,11528
%N A369787 Number of different coefficient values in expansion of Product_{k=1..n} (1+x^(k*(k+1)/2)).
%o A369787 (PARI) a(n) = #Set(Vec(prod(k=1, n, 1+x^(k*(k+1)/2))));
%o A369787 (Python)
%o A369787 from collections import Counter
%o A369787 def A369787(n):
%o A369787     c = {0:1}
%o A369787     for k in range(1,n+1):
%o A369787         m, d = k*(k+1)>>1, Counter(c)
%o A369787         for j in c:
%o A369787             d[j+m] += c[j]
%o A369787         c = d
%o A369787     return len(set(c.values()))+int(max(c)+1>len(c)) # _Chai Wah Wu_, Feb 01 2024
%Y A369787 Cf. A024940, A039822.
%K A369787 nonn
%O A369787 0,3
%A A369787 _Seiichi Manyama_, Feb 01 2024