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

1, 1, 1, 1, 2, 2, 3, 4, 5, 7, 12, 18, 27, 44, 73, 122, 210, 362, 620, 1050, 1857, 3290, 5949, 10665, 19086, 34330, 62252, 113643, 209460, 383888, 706457, 1300198, 2407535, 4468367, 8331820, 15525814, 28987902, 54180854, 101560631, 190708871, 358969426

Offset: 0

Author

Seiichi Manyama, Dec 27 2022

Keywords

• nonn

Examples

			(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.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A000217, A024940, A025591, A158380, A160235.

Programs

PARI

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

Formula

a(n) ~ sqrt(5) * 2^(n + 3/2) / (sqrt(Pi) * n^(5/2)). - Vaclav Kotesovec, Dec 29 2022