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A022168
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Triangle of Gaussian binomial coefficients [ n,k ] for q = 4.
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6
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1, 1, 1, 1, 5, 1, 1, 21, 21, 1, 1, 85, 357, 85, 1, 1, 341, 5797, 5797, 341, 1, 1, 1365, 93093, 376805, 93093, 1365, 1, 1, 5461, 1490853, 24208613, 24208613, 1490853, 5461, 1, 1, 21845, 23859109, 1550842085, 6221613541
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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REFERENCES
| F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
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LINKS
| T. D. Noe, Rows n=0..50 of triangle, flattened
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MAPLE
| A027637 := proc(n)
mul( 4^i-1, i=1..n) ;
end proc:
A022168 := proc(n, k)
A027637(n)/A027637(n-m)/A027637(m) ;
end proc: # R. J. Mathar, Nov 14 2011
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MATHEMATICA
| gaussianBinom[n_, k_, q_] := Product[q^i - 1, {i, n}]/Product[q^j - 1, {j, n - k}]/Product[q^l - 1, {l, k}]; Column[Table[gaussianBinom[n, k, 4], {n, 0, 8}, {k, 0, n}], Center] (* Alonso del Arte, Nov 14 2011 *)
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CROSSREFS
| Cf. A006118 (row sums).
Sequence in context: A036969 A080249 A157154 * A157212 A156600 A152572
Adjacent sequences: A022165 A022166 A022167 * A022169 A022170 A022171
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KEYWORD
| nonn,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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