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a(n) = 6*binomial(n,4) + 3*binomial(n,3) + 4*binomial(n,2) - n + 2.
From Colin Barker, Apr 20 2012: (Start)
a(n) = (8 - 14*n + 13*n^2 - 4*n^3 + n^4)/4. G.f.: x*(1-x+4*x^2+2*x^4)/(1-x)^5. [_Colin Barker_, Apr 20 2012]
G.f.: x*(1 - x + 4*x^2 + 2*x^4)/(1-x)^5. (End)
(PARI) { for (n=1, 1000, a=6*binomial(n, 4) + 3*binomial(n, 3) + 4*binomial(n, 2) - n + 2; write("b066375.txt", n, " ", a) ) } [From _\\ _Harry J. Smith_, Feb 11 2010]
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<a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
Table[6Binomial[n, 4]+3Binomial[n, 3]+4Binomial[n, 2]-n+2, {n, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 4, 14, 40, 97}, 40] (* Harvey P. Dale, Feb 05 2017 *)
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Harry J. Smith, <a href="/A066375/b066375.txt">Table of n, a(n) for n = 1,...,1000</a>
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a(n) = (8-14*n+13*n^2-4*n^3+n^4)/4. G.f.: x*(1-x+4*x^2+2*x^4)/(1-x)^5. [Colin Barker, Apr 20 2012]
nonn,easy
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(PARI) { for (n=1, 1000, a=6*binomial(n, 4) + 3*binomial(n, 3) + 4*binomial(n, 2) - n + 2; write("b066375.txt", n, " ", a) ) } [From _Harry J. Smith (hjsmithh(AT)sbcglobal.net), _, Feb 11 2010]