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

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

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

Magma

[n*(n+1)*(n^2-3*n+6)/8: n in [1..50]]; // Vincenzo Librandi, Jun 07 2013

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 *)

PARI

a(n)=n*(n+1)*(n^2-3*n+6)/8 \\ Charles R Greathouse IV, Oct 07 2015

Formula

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