A061224 a(n) = n^2 + (n + 1)^3 + (n + 2)^4 + (n + 3)^5.

260, 1114, 3412, 8474, 18244, 35410, 63524, 107122, 171844, 264554, 393460, 568234, 800132, 1102114, 1488964, 1977410, 2586244, 3336442, 4251284, 5356474, 6680260, 8253554, 10110052, 12286354, 14822084, 17760010, 21146164, 25029962

Offset: 0

Author

Olivier Gérard, May 31 2001

Keywords

• nonn
• easy

Examples

			a(1) = 1 + 2^3 + 3^4 + 4^5 = 1 + 8 + 81 + 1024 = 1114.
		

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. A027621.

Programs

GAP

List([0..30],n->n^2+(n+1)^3+(n+2)^4+(n+3)^5); # Muniru A Asiru, Nov 02 2018

Magma

[n^2 + (n + 1)^3 + (n + 2)^4 + (n + 3)^5: n in [0..30]]; // Vincenzo Librandi, Aug 05 2011

Maple

seq(n^2+(n+1)^3+(n+2)^4+(n+3)^5,n=0..30); # Muniru A Asiru, Nov 02 2018

Mathematica

Table[n^2 +(n+1)^3 +(n+2)^4 +(n+3)^5, {n,0,30}] (* G. C. Greubel, Nov 02 2018 *)
CoefficientList[Series[E^x (260 + 854 x + 722 x^2 + 220 x^3 + 26 x^4 + x^5), {x, 0, 50}], x]*Table[k!, {k, 0, 50}] (* Stefano Spezia, Nov 02 2018 *)
Table[260+440 n+298 n^2+99 n^3+16 n^4+n^5,{n,0,30}] (* or *) LinearRecurrence[ {6,-15,20,-15,6,-1},{260,1114,3412,8474,18244,35410},30] (* Harvey P. Dale, Nov 14 2022 *)

PARI

vector(30, n, n--; n^2 +(n+1)^3 +(n+2)^4 +(n+3)^5) \\ G. C. Greubel, Nov 02 2018

Formula

G.f.: 2*(130 - 223*x + 314*x^2 - 244*x^3 + 100*x^4 - 17*x^5)/(1-x)^6. - Bruno Berselli, Aug 05 2011

E.g.f.: exp(x)*(260 + 854*x + 722*x^2 + 220*x^3 + 26*x^4 + x^5). - Stefano Spezia, Nov 02 2018

Extensions

Offset changed from 1 to 0 by Vincenzo Librandi, Aug 05 2011