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A085786
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a(n) = n*(2*n^2 + n + 1)/2.
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4
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2, 11, 33, 74, 140, 237, 371, 548, 774, 1055, 1397, 1806, 2288, 2849, 3495, 4232, 5066, 6003, 7049, 8210, 9492, 10901, 12443, 14124, 15950, 17927, 20061, 22358, 24824, 27465, 30287, 33296, 36498, 39899, 43505, 47322, 51356, 55613, 60099, 64820
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
G.f.: x*(x+1)*(x+2) / (x-1)^4. (End)
E.g.f.: (x/2)*(4 + 7*x + 2*x^2)*exp(x). - G. C. Greubel, Aug 24 2017
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MATHEMATICA
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CoefficientList[Series[(x + 1) (x + 2) / (x - 1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {2, 11, 33, 74}, 40] (* Vincenzo Librandi, Aug 14 2017 *)
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PROG
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(PARI) t(n)=n*(n+1)/2;
vector(40, i, t(i)+i^3)
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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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EXTENSIONS
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STATUS
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approved
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