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

0,3

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.

Formula

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

Mathematica

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

Crossrefs

Cf. A277218, A022166.

Sequence in context: A363204 A204516 A331679 * A005648 A113947 A102008

Adjacent sequences: A277343 A277344 A277345 * A277347 A277348 A277349

Keyword

nonn

Author

Vladimir Reshetnikov, Oct 09 2016

Status

approved