A004255 n(n+1)(n^2 -3n + 6)/8. (Formerly M2794)

1, 3, 9, 25, 60, 126, 238, 414, 675, 1045, 1551, 2223, 3094, 4200, 5580, 7276, 9333, 11799, 14725, 18165, 22176, 26818, 32154, 38250, 45175, 53001, 61803, 71659, 82650, 94860, 108376, 123288, 139689, 157675, 177345, 198801, 222148, 247494, 274950

Offset

1,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: -x*(1-2*x+4*x^2) / (x-1)^5. - Simon Plouffe in his 1992 dissertation.

Mathematica

lst={}; Do[AppendTo[lst, n*(n+1)*(n^2-3*n+6)/8], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 19 2008 *)
Table[n(n+1)(n^2-3n+6)/8, {n, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 3, 9, 25, 60}, 40] (* Harvey P. Dale, May 27 2023 *)

Prog

(Magma) [n*(n+1)*(n^2-3*n+6)/8: n in [1..50]]; // Vincenzo Librandi, Jun 07 2013
(PARI) a(n)=n*(n+1)*(n^2-3*n+6)/8 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Partial sums of A060354. Equals (1/2) A062026.

Sequence in context: A112522 A005262 A101357 * A065971 A145127 A096260

Adjacent sequences: A004252 A004253 A004254 * A004256 A004257 A004258

Keyword

nonn,easy

Author

Dennis S. Kluk (mathemagician(AT)ameritech.net)

Status

approved