A155977 a(n) = n^5 + n^3.

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

Offset: 0

Author

Vincenzo Librandi, Feb 01 2009

Keywords

• nonn
• easy

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A000578, A002522, A168178.

Programs

GAP

List([0..30], n-> n^5 + n^3); # G. C. Greubel, Sep 02 2019

Magma

[n^5 + n^3: n in [0..30]] // Vincenzo Librandi, Feb 03 2012

Maple

seq(n^5 + n^3, n=0..30); # G. C. Greubel, Sep 02 2019

Mathematica

Table[n^5 + n^3, {n,0,30}] (* Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *)
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 *)

PARI

a(n)=n^5+n^3 \\ Charles R Greathouse IV, Dec 28 2011

Sage

[n^5 + n^3 for n in (0..30)] # G. C. Greubel, Sep 02 2019

Formula

a(n) = 2*A168178(n).

a(n) = A000578(n)*A002522(n). - Vincenzo Librandi, Feb 03 2012

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