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%I #9 Jan 07 2023 10:46:09
%S 1,1,2,3,8,16,48,119,390,1070,3656,10762,37834,116546,417540,1330923,
%T 4836452,15823388,58130756,194168612,719541996,2444224858,9121965276,
%U 31422225930,117959864244,411141476444,1551101290792,5460849893348,20689450250926,73474839110524
%N Maximal coefficient among squares of the polynomials in row n of the triangle of q-binomial coefficients.
%C q-binomial coefficients (a.k.a. Gaussian binomial coefficients) are polynomials in q with integer coefficients.
%H Vaclav Kotesovec, <a href="/A277346/b277346.txt">Table of n, a(n) for n = 0..100</a>
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/q-BinomialCoefficient.html">q-Binomial Coefficient</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Q-binomial">q-binomial</a>.
%F Conjecture: a(n) ~ sqrt(3) * 2^(2*n+2) / (Pi^(3/2) * n^(5/2)). - _Vaclav Kotesovec_, Jan 07 2023
%t Table[Max[Table[Max[CoefficientList[FunctionExpand[QBinomial[n, k, q]^2], q]], {k, 0, n}]], {n, 0, 30}]
%Y Cf. A277218, A022166.
%K nonn
%O 0,3
%A _Vladimir Reshetnikov_, Oct 09 2016
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