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Largest coefficient in expansion of Product_{i=1..n} (1-q^1+q^2-...+(-q)^i).
5

%I #24 Jan 05 2023 18:30:05

%S 1,1,2,5,20,101,573,3836,29228,250749,2409581,25380120,294625748,

%T 3727542188,50626553988,738680521142,11501573822788,190418421447330,

%U 3344822488498265,61995904304519920,1212867413232346644,24965661442811799655,538134522243713149122

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

%H Seiichi Manyama, <a href="/A039909/b039909.txt">Table of n, a(n) for n = 0..200</a>

%F Conjecture: a(n) ~ 6 * n^n / exp(n). - _Vaclav Kotesovec_, Jan 05 2023

%o (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

%o (PARI) a(n) = vecmax(Vec(prod(j=1, n, sum(k=0, j, (-x)^k)))); \\ _Seiichi Manyama_, Jan 05 2023

%Y Cf. A000140, A039828, A039830.

%K nonn

%O 0,3

%A _Olivier GĂ©rard_

%E a(0)=1 prepended by _Seiichi Manyama_, Jan 05 2023