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URL: https://oeis.org/A027622

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A027622
a(n) = n + (n+1)^2 + (n+2)^3 + (n+3)^4 + (n+4)^5.
4
1114, 3413, 8476, 18247, 35414, 63529, 107128, 171851, 264562, 393469, 568244, 800143, 1102126, 1488977, 1977424, 2586259, 3336458, 4251301, 5356492, 6680279, 8253574, 10110073, 12286376, 14822107, 17760034, 21146189, 25029988, 29464351, 34505822, 40214689
OFFSET
0,1
FORMULA
From Colin Barker, Dec 05 2016: (Start)
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.
G.f.: (1114-3271*x+4708*x^2-3694*x^3+1522*x^4-259*x^5) / (1-x)^6.
(End)
E.g.f.: (1114 +2299*x +1382*x^2 +324*x^3 +31*x^4 +x^5)*exp(x). - G. C. Greubel, Aug 05 2022
MAPLE
seq( add((n+j)^(j+1), j=0..4), n=0..30); # G. C. Greubel, Aug 05 2022
MATHEMATICA
Table[n +(n+1)^2 +(n+2)^3 +(n+3)^4 +(n+4)^5, {n, 0, 29}] (* Alonso del Arte, Nov 22 2016 *)
Table[ReleaseHold@ Total@ MapIndexed[#1^First@ #2 &, Rest@ FactorList[ Pochhammer[Hold@ n, 5]][[All, 1]]], {n, 0, 29}] (* or *)
CoefficientList[Series[(1114 -3271x +4708x^2 -3694x^3 +1522x^4 -259x^5)/(1-x)^6, {x, 0, 29}], x] (* Michael De Vlieger, Dec 05 2016 *)
Table[Total[Table[(n+k)^(k+1), {k, 0, 4}]], {n, 0, 30}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1114, 3413, 8476, 18247, 35414, 63529}, 30] (* Harvey P. Dale, Aug 04 2022 *)
PROG
(Magma)[n+(n+1)^2+(n+2)^3+(n+3)^4+(n+4)^5: n in [0..30]]; // Vincenzo Librandi, Dec 28 2010
(PARI) Vec((1114-3271*x+4708*x^2-3694*x^3+1522*x^4-259*x^5) / (1-x)^6 + O(x^30)) \\ Colin Barker, Dec 05 2016
(SageMath) [sum((n+j)^(j+1) for j in (0..4)) for n in (0..30)] # G. C. Greubel, Aug 05 2022
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved