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A277271
Second largest coefficient among the polynomials in row n of the triangle of q-binomial coefficients.
0
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved