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A006334
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From the enumeration of corners.
(Formerly M2179)
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2
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0, 2, 110, 2002, 20020, 136136, 705432, 2984520, 10786908, 34370050, 98768670, 260390130, 638110200, 1468635168, 3200871520, 6650874912, 13248113736, 25415833170, 47143878782, 84832157410, 148507792972, 253549890440, 423093671000, 691331713800, 1107985378500
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
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FORMULA
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a(n) = (n*(1 + n)^2*(2 + n)^2*(3 + n)^2*(4 + n)*(1 + 2*n)*(3 + 2*n)*(5 + 2*n)*(7 + 2*n))/1360800.
G.f.: -2*x*(x+1)*(x^6 + 41*x^5 + 323*x^4 + 678*x^3 + 323*x^2 + 41*x + 1)/(x-1)^13. - Colin Barker, Sep 19 2012
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MATHEMATICA
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Abs@ With[{n = 5}, Table[(2 (-1)^(n + k) (n + k - 1)! (2 n + 2 k - 3)!)/(n! k! (2 n - 1)! (2 k - 1)!), {k, 0, 24}]] (* Michael De Vlieger, Mar 26 2016 *)
LinearRecurrence[{13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1}, {0, 2, 110, 2002, 20020, 136136, 705432, 2984520, 10786908, 34370050, 98768670, 260390130, 638110200}, 30] (* Harvey P. Dale, Apr 21 2016 *)
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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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