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

1, 1, 2, 4, 7, 11, 19, 30, 55, 90, 166, 285, 519, 902, 1656, 2929, 5424, 9673, 18012, 32467, 60981, 110599, 208445, 381301, 722552, 1327869, 2522994, 4665786, 8902311, 16524759, 31594853, 58935171, 113038371, 211499060, 406350261, 763246536, 1470080699

Offset

4,3

Comments

q-binomial coefficients are polynomials in q with integer coefficients.

Links

Table of n, a(n) for n=4..40.

Eric W. Weisstein, q-Binomial Coefficient

Wikipedia, q-binomial

Example

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.

Mathematica

Table[(Union @@ Table[CoefficientList[FunctionExpand[QBinomial[n, k, q]], q], {k, 0, n}])[[-2]], {n, 4, 40}]

Crossrefs

Cf. A002838, A022166, A029895, A055606, A076822, A277218 (largest coefficients).

Sequence in context: A083024 A003292 A007864 * A192670 A118647 A000802

Adjacent sequences: A277268 A277269 A277270 * A277272 A277273 A277274

Keyword

nonn

Author

Vladimir Reshetnikov, Oct 07 2016

Status

approved