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A057658
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a(n) = n*(n+1)^2*(n+2)^3*(n+3)^2*(n+4).
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1
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0, 8640, 172800, 1512000, 8467200, 35562240, 121927680, 359251200, 940896000, 2242468800, 4947022080, 10231341120, 20033395200, 37425024000, 67118284800, 116138603520, 194702952960, 317346724800, 504348768000, 783510235200
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45, 10,-1).
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FORMULA
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G.f.: 8640*x*(x^4 + 10*x^3 + 20*x^2 + 10*x + 1)/(x - 1)^10.
(n + 3)*(n + 2)*a(n - 2) - 2*(n^2 + 2*n + 12)*a(n - 1) + n*(n - 1)*a(n) = 0. (End)
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MAPLE
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seq(n*(n+1)^2*(n+2)^3*(n+3)^2*(n+4), n=0..30); # Robert Israel, Jun 06 2019
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MATHEMATICA
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Table[n (n+1)^2 (n+2)^3 (n+3)^2 (n+4), {n, 0, 40}] (* Vincenzo Librandi, Jun 07 2019 *)
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 8640, 172800, 1512000, 8467200, 35562240, 121927680, 359251200, 940896000, 2242468800}, 30] (* Harvey P. Dale, Sep 24 2021 *)
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PROG
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(Magma) [n*(n+1)^2*(n+2)^3*(n+3)^2*(n+4): n in [0..25]]; // Vincenzo Librandi, Jun 07 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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