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A167925
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Triangle, T(n, k) = (sqrt(k+1))^(n-1)*ChebyshevU(n-1, sqrt(k+1)/2), read by rows.
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2
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0, 1, 1, 1, 2, 3, 0, 2, 6, 12, -1, 0, 9, 32, 75, -1, -4, 9, 80, 275, 684, 0, -8, 0, 192, 1000, 3240, 8232, 1, -8, -27, 448, 3625, 15336, 47677, 122368, 1, 0, -81, 1024, 13125, 72576, 276115, 835584, 2158569, 0, 16, -162, 2304, 47500, 343440, 1599066, 5705728, 16953624, 44010000
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OFFSET
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0,5
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LINKS
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FORMULA
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T(n, k) = (sqrt(k+1))^(n-1)*ChebyshevU(n-1, sqrt(k+1)/2).
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EXAMPLE
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Triangle begins as:
0;
1, 1;
1, 2, 3;
0, 2, 6, 12;
-1, 0, 9, 32, 75;
-1, -4, 9, 80, 275, 684;
0, -8, 0, 192, 1000, 3240, 8232;
1, -8, -27, 448, 3625, 15336, 47677, 122368;
1, 0, -81, 1024, 13125, 72576, 276115, 835584, 2158569;
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MATHEMATICA
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(* First program *)
m[k_]= {{k, 1}, {-1, 1}};
v[0, k_]:= {0, 1};
v[n_, k_]:= v[n, k]= m[k].v[n-1, k];
T[n_, k_]:= v[n, k][[1]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
(* Second program *)
A167925[n_, k_]:= (Sqrt[k+1])^(n-1)*ChebyshevU[n-1, Sqrt[k+1]/2];
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PROG
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(Magma)
A167925:= func< n, k | Round((Sqrt(k+1))^(n-1)*Evaluate(ChebyshevSecond(n), Sqrt(k+1)/2)) >;
(SageMath)
def A167925(n, k): return (sqrt(k+1))^(n-1)*chebyshev_U(n-1, sqrt(k+1)/2)
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CROSSREFS
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Cf. A009545, A030191, A030192, A030240, A057083, A057084, A057085, A057086, A099087, A128834, A190871, A190873.
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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