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A327319
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a(n) = binomial(n, 2) + 6*binomial(n, 4).
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1
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0, 0, 1, 3, 12, 40, 105, 231, 448, 792, 1305, 2035, 3036, 4368, 6097, 8295, 11040, 14416, 18513, 23427, 29260, 36120, 44121, 53383, 64032, 76200, 90025, 105651, 123228, 142912, 164865, 189255, 216256, 246048, 278817, 314755, 354060, 396936
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OFFSET
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0,4
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LINKS
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FORMULA
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G.f.: x^2*(1 - 2*x + 7*x^2) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>4.
a(n) = (n*(-8 + 13*n - 6*n^2 + n^3)) / 4.
(End)
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EXAMPLE
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a(5) = binomial(5, 2) + 6*binomial(5, 4) = 10 + 6*5 = 40.
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MATHEMATICA
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Table[Binomial[n, 2] + 6Binomial[n, 4], {n, 0, 39}] (* Alonso del Arte, Sep 18 2019 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 1, 3, 12}, 40] (* Harvey P. Dale, Dec 10 2022 *)
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PROG
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(PARI) a(n) = {binomial(n, 2) + 6 * binomial(n, 4)} \\ Andrew Howroyd, Sep 20 2019
(PARI) concat([0, 0], Vec(x^2*(1 - 2*x + 7*x^2) / (1 - x)^5 + O(x^40))) \\ Colin Barker, Sep 25 2019
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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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