A039909 Largest coefficient in expansion of Product_{i=1..n} (1-q^1+q^2-...+(-q)^i).

1, 1, 2, 5, 20, 101, 573, 3836, 29228, 250749, 2409581, 25380120, 294625748, 3727542188, 50626553988, 738680521142, 11501573822788, 190418421447330, 3344822488498265, 61995904304519920, 1212867413232346644, 24965661442811799655, 538134522243713149122

Offset

0,3

Links

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

Formula

Conjecture: a(n) ~ 6 * n^n / exp(n). - Vaclav Kotesovec, Jan 05 2023

Prog

(Magma) PS<q>:=PowerSeriesRing(Integers()); [ Max(Coefficients(&*[&+[ (-q)^i: i in [0..j] ]: j in [0..n] ])): n in [1..20] ]; // Klaus Brockhaus, Jan 18 2011
(PARI) a(n) = vecmax(Vec(prod(j=1, n, sum(k=0, j, (-x)^k)))); \\ Seiichi Manyama, Jan 05 2023

Crossrefs

Cf. A000140, A039828, A039830.

Sequence in context: A020001 A348597 A370699 * A009551 A323274 A006924

Adjacent sequences: A039906 A039907 A039908 * A039910 A039911 A039912

Keyword

nonn

Author

Olivier Gérard

Extensions

a(0)=1 prepended by Seiichi Manyama, Jan 05 2023

Status

approved