OFFSET
0,1
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Patrick De Geest, Palindromic Quasi_Under_Squares of the form n+(n+1)^2
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-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
AUTHOR
STATUS
approved