A277346 Maximal coefficient among squares of the polynomials in row n of the triangle of q-binomial coefficients.

1, 1, 2, 3, 8, 16, 48, 119, 390, 1070, 3656, 10762, 37834, 116546, 417540, 1330923, 4836452, 15823388, 58130756, 194168612, 719541996, 2444224858, 9121965276, 31422225930, 117959864244, 411141476444, 1551101290792, 5460849893348, 20689450250926, 73474839110524

Offset: 0

Author

Vladimir Reshetnikov, Oct 09 2016

Keywords

• nonn

Comments

q-binomial coefficients (a.k.a. Gaussian binomial coefficients) are polynomials in q with integer coefficients.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..100
• Eric W. Weisstein, q-Binomial Coefficient.
• Wikipedia, q-binomial.

Crossrefs

Cf. A277218, A022166.

Programs

Mathematica

Table[Max[Table[Max[CoefficientList[FunctionExpand[QBinomial[n, k, q]^2], q]], {k, 0, n}]], {n, 0, 30}]

Formula

Conjecture: a(n) ~ sqrt(3) * 2^(2*n+2) / (Pi^(3/2) * n^(5/2)). - Vaclav Kotesovec, Jan 07 2023