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A359320 Maximal coefficient of (1 + x) * (1 + x^16) * (1 + x^81) * ... * (1 + x^(n^4)).

%I A359320 #20 Jan 31 2024 14:12:16
%S A359320 1,1,1,1,1,1,1,1,1,2,2,3,3,4,5,5,6,9,13,17,24,34,53,84,130,177,290,
%T A359320 500,797,1300,2066,3591,6090,10298,17330,29888,50811,88358,153369,
%U A359320 280208,481289,845090,1474535,2703811,4808816,8329214,14806743,27529781,48859783,87674040,156471632
%N A359320 Maximal coefficient of (1 + x) * (1 + x^16) * (1 + x^81) * ... * (1 + x^(n^4)).
%H A359320 Vaclav Kotesovec, <a href="/A359320/b359320.txt">Table of n, a(n) for n = 0..100</a>
%p A359320 f:= proc(n) local i; max(coeffs(expand(mul(1+x^(i^4), i=1..n)))) end proc:
%p A359320 map(f, [$1..50]); # _Robert Israel_, Dec 26 2022
%o A359320 (PARI) a(n) = vecmax(Vec(prod(k=1, n, 1+x^(k^4)))); \\ _Michel Marcus_, Dec 26 2022
%o A359320 (Python)
%o A359320 from collections import Counter
%o A359320 def A359320(n):
%o A359320     c = {0:1,1:1}
%o A359320     for i in range(2,n+1):
%o A359320         j, d = i**4, Counter(c)
%o A359320         for k in c:
%o A359320             d[k+j] += c[k]
%o A359320         c = d
%o A359320     return max(c.values()) # _Chai Wah Wu_, Jan 31 2024
%Y A359320 Cf. A000538, A000583, A025591, A160235, A298859, A359319.
%K A359320 nonn
%O A359320 0,10
%A A359320 _Ilya Gutkovskiy_, Dec 25 2022
%E A359320 a(38)-a(50) from _Seiichi Manyama_, Dec 26 2022