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

1, 1, 2, 2, 3, 3, 4, 5, 6, 8, 13, 19, 28, 44, 71, 112, 168, 249, 321, 419, 549, 652, 797, 939, 1104, 1265, 1440, 1638, 1842, 2059, 2295, 2538, 2809, 3087, 3385, 3698, 4032, 4381, 4754, 5143, 5554, 5985, 6437, 6910, 7405, 7922, 8463, 9027, 9615, 10227, 10865, 11528

Offset: 0

Author

Seiichi Manyama, Feb 01 2024

Keywords

• nonn

Crossrefs

Cf. A024940, A039822.

Programs

PARI

a(n) = #Set(Vec(prod(k=1, n, 1+x^(k*(k+1)/2))));

Python

from collections import Counter
def A369787(n):
    c = {0:1}
    for k in range(1,n+1):
        m, d = k*(k+1)>>1, Counter(c)
        for j in c:
            d[j+m] += c[j]
        c = d
    return len(set(c.values()))+int(max(c)+1>len(c)) # Chai Wah Wu, Feb 01 2024