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 A277218 Maximal coefficient among the polynomials in row n of the triangle of q-binomial coefficients. 5
 1, 1, 1, 1, 2, 2, 3, 5, 8, 12, 20, 32, 58, 94, 169, 289, 526, 910, 1667, 2934, 5448, 9686, 18084, 32540, 61108, 110780, 208960, 381676, 723354, 1328980, 2527074, 4669367, 8908546, 16535154, 31630390, 58965214, 113093022, 211591218, 406680465, 763535450, 1470597342, 2769176514, 5342750699, 10089240974 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS q-binomial coefficients are polynomials in q with integer coefficients. Is A055606 a shifted version of this sequence? LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..200 E. Friedman and M. Keith, Magic Carpets, J. Int Sequences, 3 (2000), #P.00.2.5. Eric W. Weisstein, q-Binomial Coefficient Wikipedia, q-binomial FORMULA a(n) ~ sqrt(3) * 2^(n+2) / (Pi * n^2). - Vaclav Kotesovec, Oct 09 2016 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], so the max coefficient is 2. Hence a(5) = 2. MAPLE f:= proc(n) local k, c, v, q; uses QDifferenceEquations; v:= 0: for k from 0 to n do c:= coeffs(expand(expand(QBinomial(n, k, q))), q); v:= max(v, max(c)); od: v end proc: map(f, [\$0..50]); # Robert Israel, Oct 05 2016 MATHEMATICA Table[Coefficient[Expand[FunctionExpand[QBinomial[n, Floor[n/2], q]]], q, Floor[n^2/8]], {n, 0, 30}] (* Vladimir Reshetnikov, Sep 24 2021 *) CROSSREFS Cf. A002838, A022166, A029895, A055606, A076822. Sequence in context: A018136 A243853 A293419 * A293643 A022863 A236393 Adjacent sequences: A277215 A277216 A277217 * A277219 A277220 A277221 KEYWORD nonn AUTHOR Vladimir Reshetnikov, Oct 05 2016 STATUS approved

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Last modified April 18 22:18 EDT 2024. Contains 371782 sequences. (Running on oeis4.)