A369710 -id:A369710 - cp's OEIS frontend

A380499 Absolute value of the minimum coefficient of (1 - x)^2 * (1 - x^2)^2 * (1 - x^3)^2 * ... * (1 - x^n)^2.

1, 2, 2, 6, 4, 12, 8, 24, 19, 44, 36, 78, 74, 148, 156, 286, 322, 556, 682, 1120, 1448, 2308, 3072, 4784, 6538, 10064, 14001, 21296, 29928, 45276, 64032, 96712, 137520, 207156, 296236, 444748, 637812, 956884, 1373622, 2062080, 2968872, 4450120, 6422472, 9616202, 13894990, 20802836

Offset: 0

Ilya Gutkovskiy, Jan 25 2025

nonn

Cf. A002107, A047653, A086394, A133871, A369710.

p:= proc(n) option remember;
     `if`(n=0, 1, expand(p(n-1)*(1-x^n)^2))
    end:
a:= n-> abs(min(coeffs(p(n)))):
seq(a(n), n=0..45);  # Alois P. Heinz, Jan 25 2025

Table[Min[CoefficientList[Product[(1 - x^k)^2, {k, 1, n}], x]], {n, 0, 45}] // Abs

a(n) = abs(vecmin(Vec(prod(k=1, n, (1-x^k)^2)))); \\ Michel Marcus, Jan 25 2025

A369726 Maximal coefficient of (1 - x) * (1 - x^2)^2 * (1 - x^3)^3 * ... * (1 - x^n)^n.

Original entry on oeis.org

1, 1, 2, 5, 30, 289, 5170, 155768, 7947236, 695357704, 105014923458, 26823702973095, 12124672181643014, 9302296598744837059, 12142590791028740988194, 26874517085010633423659616, 100413718348008543669377307304, 634527279123990475683817934978079

Offset: 0

Ilya Gutkovskiy, Jan 30 2024

nonn

Cf. A073592, A086376, A369710, A369711, A369712.

a:= n-> max(coeffs(expand(mul((1-x^k)^k, k=1..n)))):
seq(a(n), n=0..17);  # Alois P. Heinz, Jan 30 2024

Table[Max[CoefficientList[Product[(1 - x^k)^k, {k, 1, n}], x]], {n, 0, 17}]

a(n) = vecmax(Vec(prod(k=1, n, (1-x^k)^k))); \\ Michel Marcus, Jan 30 2024

A369727 Maximal coefficient of ( (1 - x) * (1 - x^2) * (1 - x^3) * ... * (1 - x^n) )^n.

Original entry on oeis.org

1, 1, 4, 15, 226, 2630, 95420, 4177117, 371458250, 49558386762, 11496848193144, 4055873729544890, 2321900139799896688, 2052844416093203835934, 2864423943667784141723196, 6181759121650271558049171285, 20773297302068160010868731066114

Offset: 0

Ilya Gutkovskiy, Jan 30 2024

nonn

Cf. A008705, A086376, A369710, A369711, A369725.

Table[Max[CoefficientList[Product[(1 - x^k)^n, {k, 1, n}], x]], {n, 0, 16}]

a(n) = vecmax(Vec(prod(k=1, n, (1-x^k))^n)); \\ Michel Marcus, Jan 30 2024

cp's OEIS Frontend

A380499 Absolute value of the minimum coefficient of (1 - x)^2 * (1 - x^2)^2 * (1 - x^3)^2 * ... * (1 - x^n)^2.

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A369726 Maximal coefficient of (1 - x) * (1 - x^2)^2 * (1 - x^3)^3 * ... * (1 - x^n)^n.

Views

Author

Keywords

Crossrefs

Programs

Maple

Mathematica

PARI

A369727 Maximal coefficient of ( (1 - x) * (1 - x^2) * (1 - x^3) * ... * (1 - x^n) )^n.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI