|
%I #34 Sep 08 2022 08:45:41
%S 0,2,40,270,1088,3250,7992,17150,33280,59778,101000,162382,250560,
%T 373490,540568,762750,1052672,1424770,1895400,2482958,3208000,4093362,
%U 5164280,6448510,7976448,9781250,11898952,14368590,17232320,20535538
%N a(n) = n^5 + n^3.
%C 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
%H Vincenzo Librandi, <a href="/A155977/b155977.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(n) = 2*A168178(n).
%F a(n) = A000578(n)*A002522(n). - _Vincenzo Librandi_, Feb 03 2012
%F G.f.: 2*x*(1 + 14*x + 30*x^2 + 14*x^3 + x^4)/(1-x)^6. - _Vincenzo Librandi_, Feb 05 2013
%F E.g.f.: x*(2 + 18*x + 26*x^2 + 10*x^3 + x^4)*exp(x). - _G. C. Greubel_, Sep 02 2019
%p seq(n^5 + n^3, n=0..30); # _G. C. Greubel_, Sep 02 2019
%t Table[n^5 + n^3, {n,0,30}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 18 2011 *)
%t CoefficientList[Series[2x(1+14x+30x^2+14x^3+x^4)/(1-x)^6, {x,0,30}], x] (* _Vincenzo Librandi_, Feb 05 2013 *)
%t LinearRecurrence[{6,-15,20,-15,6,-1}, {0,2,40,270,1088,3250}, 30] (* _Harvey P. Dale_, Jan 18 2015 *)
%o (PARI) a(n)=n^5+n^3 \\ _Charles R Greathouse IV_, Dec 28 2011
%o (Magma) [n^5 + n^3: n in [0..30]] // _Vincenzo Librandi_, Feb 03 2012
%o (Sage) [n^5 + n^3 for n in (0..30)] # _G. C. Greubel_, Sep 02 2019
%o (GAP) List([0..30], n-> n^5 + n^3); # _G. C. Greubel_, Sep 02 2019
%Y Cf. A000578, A002522, A168178.
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Feb 01 2009
|
