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A079034
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Determinant of M(n), the n X n matrix defined by m(i,i)=1, m(i,j)=i-j.
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3
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1, 2, 7, 21, 51, 106, 197, 337, 541, 826, 1211, 1717, 2367, 3186, 4201, 5441, 6937, 8722, 10831, 13301, 16171, 19482, 23277, 27601, 32501, 38026, 44227, 51157, 58871, 67426, 76881, 87297, 98737, 111266, 124951, 139861, 156067, 173642, 192661
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OFFSET
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1,2
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COMMENTS
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Starting (1, 1, 2, 7, 21, 51, 106, ...), = Narayana transform (A001263) of [1, 0, 1, 0, 0, 0, ...]. - Gary W. Adamson, Jan 04 2008
In 2022, Han Wang and Zhi-Wei Sun provided a proof of the formula a(n) = 1 + n^2*(n^2-1)/12 via eigenvalues. See A355175 for my conjecture on det[(i-j)^2+d(i,j)]_{1<=i,j<=n}, where d(i,j) is 1 or 0 according as i = j or not. - Zhi-Wei Sun, Jun 28 2022
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LINKS
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FORMULA
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a(n) = (n^4-n^2+12)/12; a(n) = A002415(n)+1.
G.f.: -x*(x^4-4*x^3+7*x^2-3*x+1) / (x-1)^5. - Colin Barker, Jun 24 2013
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MATHEMATICA
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LinearRecurrence[{5, -10, 10, -5, 1}, {1, 2, 7, 21, 51}, 50] (* Harvey P. Dale, Aug 17 2014 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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