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A327319
a(n) = binomial(n, 2) + 6*binomial(n, 4).
1
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
OFFSET
0,4
FORMULA
From Colin Barker, Sep 21 2019: (Start)
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)
E.g.f.: (1/4)*exp(x)*x^2*(2 + x^2). - Stefano Spezia, Sep 21 2019
EXAMPLE
a(5) = binomial(5, 2) + 6*binomial(5, 4) = 10 + 6*5 = 40.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A032093 A007993 A293366 * A080929 A052482 A061136
KEYWORD
nonn,easy
AUTHOR
Aaron Kemats, Sep 17 2019
STATUS
approved