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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
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
Sequence in context: A018136 A243853 A293419 * A293643 A022863 A236393
KEYWORD
nonn
AUTHOR
STATUS
approved

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