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A323012
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a(n) = (1/sqrt(n^2+1)) * T_{2*n+1}(sqrt(n^2+1)) where T_{n}(x) is a Chebyshev polynomial of the first kind.
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2
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1, 5, 305, 53353, 18674305, 10928351501, 9616792908241, 11868363584907985, 19553538801258341377, 41456387654578883552149, 109939727677547706703222001, 356521758767660233608385698361, 1387930545993760882531890016305025
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} binomial(2*n+1,2*k)*(n^2+1)^(n-k)*n^(2*k).
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MATHEMATICA
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Join[{1}, Table[Sum[Binomial[2 n + 1, 2 k] (n^2 + 1)^(n - k) n^(2 k), {k, 0, n}], {n, 20}]] (* Vincenzo Librandi, Jan 03 2019 *)
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PROG
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(PARI) {a(n) = sum(k=0, n, binomial(2*n+1, 2*k)*(n^2+1)^(n-k)*n^(2*k))}
(Magma) [&+[Binomial(2*n+1, 2*k)*(n^2+1)^(n-k)*n^(2*k): k in [0..n]]: n in [0..15]]; // Vincenzo Librandi, Jan 03 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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