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A272866
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Triangle read by rows, T(n,k) = GegenbauerC(m,-n,-3/2) where m = k if k<n else 2*n-k, for n>=0 and 0<=k<=2n.
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2
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1, 1, 3, 1, 1, 6, 11, 6, 1, 1, 9, 30, 45, 30, 9, 1, 1, 12, 58, 144, 195, 144, 58, 12, 1, 1, 15, 95, 330, 685, 873, 685, 330, 95, 15, 1, 1, 18, 141, 630, 1770, 3258, 3989, 3258, 1770, 630, 141, 18, 1, 1, 21, 196, 1071, 3801, 9198, 15533, 18483, 15533, 9198, 3801, 1071, 196, 21, 1
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OFFSET
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0,3
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COMMENTS
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These are the antidiagonals of the following array with the bivariate generating function 1/(1-x^2-3*x*y-y^2):
1 0 1 0 1 0 1 0 1 0 1 ...
0 3 0 6 0 9 0 12 0 15 0 ...
1 0 11 0 30 0 58 0 95 0 141 ...
0 6 0 45 0 144 0 330 0 630 0 ...
1 0 30 0 195 0 685 0 1770 0 3801 ...
0 9 0 144 0 873 0 3258 0 9198 0 ...
1 0 58 0 685 0 3989 0 15533 0 46928 ...
0 12 0 330 0 3258 0 18483 0 74280 0 ...
1 0 95 0 1770 0 15533 0 86515 0 356283 ...
0 15 0 630 0 9198 0 74280 0 408105 0 ...
1 0 141 0 3801 0 46928 0 356283 0 1936881 ... (End)
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LINKS
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FORMULA
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EXAMPLE
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1;
1, 3, 1;
1, 6, 11, 6, 1;
1, 9, 30, 45, 30, 9, 1;
1, 12, 58, 144, 195, 144, 58, 12, 1;
1, 15, 95, 330, 685, 873, 685, 330, 95, 15, 1;
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MAPLE
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T := (n, k) -> simplify(GegenbauerC(`if`(k<n, k, 2*n-k), -n, -3/2)):
for n from 0 to 6 do seq(T(n, k), k=0..2*n) od;
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MATHEMATICA
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Table[If[n == 0, 1, GegenbauerC[If[k < n, k, 2 n - k], -n, -3/2]], {n, 0, 7}, {k, 0, 2 n}] // Flatten (* Michael De Vlieger, Aug 02 2019 *)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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