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A155977
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a(n) = n^5 + n^3.
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6
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0, 2, 40, 270, 1088, 3250, 7992, 17150, 33280, 59778, 101000, 162382, 250560, 373490, 540568, 762750, 1052672, 1424770, 1895400, 2482958, 3208000, 4093362, 5164280, 6448510, 7976448, 9781250, 11898952, 14368590, 17232320, 20535538
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OFFSET
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0,2
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COMMENTS
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Sequence occurs in the binomial identity Sum_{k = 0..n} a(k)* binomial(n,k)/binomial(n+k,k) = n^3. - Peter Bala, Feb 12 2019
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LINKS
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FORMULA
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G.f.: 2*x*(1 + 14*x + 30*x^2 + 14*x^3 + x^4)/(1-x)^6. - Vincenzo Librandi, Feb 05 2013
E.g.f.: x*(2 + 18*x + 26*x^2 + 10*x^3 + x^4)*exp(x). - G. C. Greubel, Sep 02 2019
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MAPLE
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MATHEMATICA
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CoefficientList[Series[2x(1+14x+30x^2+14x^3+x^4)/(1-x)^6, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 05 2013 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 2, 40, 270, 1088, 3250}, 30] (* Harvey P. Dale, Jan 18 2015 *)
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PROG
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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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