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A359348 Maximal coefficient of (1 + x) * (1 + x^3) * (1 + x^6) * ... * (1 + x^(n*(n+1)/2)).

%I A359348 #16 Dec 29 2022 03:04:34
%S A359348 1,1,1,1,2,2,3,4,5,7,12,18,27,44,73,122,210,362,620,1050,1857,3290,
%T A359348 5949,10665,19086,34330,62252,113643,209460,383888,706457,1300198,
%U A359348 2407535,4468367,8331820,15525814,28987902,54180854,101560631,190708871,358969426
%N A359348 Maximal coefficient of (1 + x) * (1 + x^3) * (1 + x^6) * ... * (1 + x^(n*(n+1)/2)).
%H A359348 Seiichi Manyama, <a href="/A359348/b359348.txt">Table of n, a(n) for n = 0..200</a>
%F A359348 a(n) ~ sqrt(5) * 2^(n + 3/2) / (sqrt(Pi) * n^(5/2)). - _Vaclav Kotesovec_, Dec 29 2022
%e A359348 (1 + x) * (1 + x^3) * (1 + x^6) * (1 + x^10) = 1 + x + x^3 + x^4 + x^6 + x^7 + x^9 + 2 * x^10 + x^11 + x^13 + x^14 + x^16 + x^17 + x^19 + x^20. So a(4) = 2.
%o A359348 (PARI) a(n) = vecmax(Vec(prod(k=1, n, 1+x^(k*(k+1)/2))));
%Y A359348 Cf. A000217, A024940, A025591, A158380, A160235.
%K A359348 nonn
%O A359348 0,5
%A A359348 _Seiichi Manyama_, Dec 27 2022