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A277271 Second largest coefficient among the polynomials in row n of the triangle of q-binomial coefficients.

%I A277271 #12 Feb 16 2025 08:33:36
%S A277271 1,1,2,4,7,11,19,30,55,90,166,285,519,902,1656,2929,5424,9673,18012,
%T A277271 32467,60981,110599,208445,381301,722552,1327869,2522994,4665786,
%U A277271 8902311,16524759,31594853,58935171,113038371,211499060,406350261,763246536,1470080699
%N A277271 Second largest coefficient among the polynomials in row n of the triangle of q-binomial coefficients.
%C A277271 q-binomial coefficients are polynomials in q with integer coefficients.
%H A277271 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/q-BinomialCoefficient.html">q-Binomial Coefficient</a>
%H A277271 Wikipedia, <a href="http://en.wikipedia.org/wiki/Q-binomial">q-binomial</a>
%e A277271 Row 5 of the triangle of q-binomial coefficients is [1, 1 + q + q^2 + q^3 + q^4, 1 + q + 2*q^2 + 2*q^3 + 2*q^4 + q^5 + q^6, 1 + q + 2*q^2 + 2*q^3 + 2*q^4 + q^5 + q^6, 1 + q + q^2 + q^3 + q^4, 1]. The largest coefficient is 2, and the second largest coefficient is 1. Hence A277218(5) = 2 and a(5) = 1.
%t A277271 Table[(Union @@ Table[CoefficientList[FunctionExpand[QBinomial[n, k, q]], q], {k, 0, n}])[[-2]], {n, 4, 40}]
%Y A277271 Cf. A002838, A022166, A029895, A055606, A076822, A277218 (largest coefficients).
%K A277271 nonn
%O A277271 4,3
%A A277271 _Vladimir Reshetnikov_, Oct 07 2016