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A154696
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Triangular sequence defined by T(n, m) = (r^(n-m)*q^m + r^m*q^(n-m))*b(n), where b(n) = coefficients of p(x, n) = 2^n*(1-x)^(n+1) * LerchPhi(x, -n, 1/2), and r=2, q=3.
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2
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2, 5, 5, 13, 72, 13, 35, 690, 690, 35, 97, 5928, 16560, 5928, 97, 275, 49770, 302760, 302760, 49770, 275, 793, 420204, 4934124, 10172736, 4934124, 420204, 793, 2315, 3595350, 76427820, 280500840, 280500840, 76427820, 3595350, 2315
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OFFSET
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0,1
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LINKS
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FORMULA
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Let r = 2 and q = 3 then b(n) = the coefficients of p(x, n) = 2^n*(1 - x)^(n + 1)* LerchPhi(x, -n, 1/2). The triangle is then defined by T(n, m) = (r^(n-m)*q^m + r^m*q^(n-m))*b(n).
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EXAMPLE
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Triangle begins as:
2;
5, 5;
13, 72, 13;
35, 690, 690, 35;
97, 5928, 16560, 5928, 97;
275, 49770, 302760, 302760, 49770, 275;
793, 420204, 4934124, 10172736, 4934124, 420204, 793;
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MATHEMATICA
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r = 2; q = 3; p[x_, n_] = 2^n*(1-x)^(n+1)*LerchPhi[x, -n, 1/2];
b:= Table[CoefficientList[Series[p[x, n], {x, 0, 30}], x], {n, 0, 20}];
T[n_, m_]:= (r^(n-m)*q^m + r^m*q^(n-m))*b[[n+1]][[m+1]];
Table[T[n, m], {n, 0, 12}, {m, 0, n}]//Flatten (* modified by G. C. Greubel, May 08 2019 *)
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CROSSREFS
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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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