A026057 a(n) = n*(n^2 + 12*n - 25)/6.

0, -2, 1, 10, 26, 50, 83, 126, 180, 246, 325, 418, 526, 650, 791, 950, 1128, 1326, 1545, 1786, 2050, 2338, 2651, 2990, 3356, 3750, 4173, 4626, 5110, 5626, 6175, 6758, 7376, 8030, 8721, 9450, 10218, 11026, 11875, 12766, 13700, 14678, 15701, 16770, 17886, 19050

Offset

0,2

Comments

For n >= 4, this is dot_product(n,n-1,...2,1)*(4,5,...,n,1,2,3).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

G.f.: x*(-2 +9*x -6*x^2)/(1-x)^4. - Colin Barker, Sep 17 2012

E.g.f.: x*(-12 +15*x +x^2)*exp(x)/6. - G. C. Greubel, Oct 30 2019

Maple

seq(n*(n^2+12*n-25)/6, n=0..60); # G. C. Greubel, Oct 30 2019

Mathematica

CoefficientList[Series[x(-2 +9x -6x^2)/(1-x)^4, {x, 0, 60}], x] (* Vincenzo Librandi, Oct 17 2013 *)
Table[n (n^2+12n-25)/6, {n, 0, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, -2, 1, 10}, 50] (* Harvey P. Dale, Jan 28 2020 *)

Prog

(Magma) [n*(n^2+12*n-25)/6: n in [0..60]]; // Vincenzo Librandi, Oct 17 2013
(PARI) a(n)=n*(n^2+12*n-25)/6 \\ Charles R Greathouse IV, Oct 07 2015
(Sage) [n*(n^2+12*n-25)/6 for n in (0..60)] # G. C. Greubel, Oct 30 2019
(GAP) List([0..60], n-> n*(n^2+12*n-25)/6); # G. C. Greubel, Oct 30 2019

Crossrefs

Cf. column 3 of triangle A094415.

Sequence in context: A136205 A327923 A024433 * A309234 A071926 A133103

Adjacent sequences: A026054 A026055 A026056 * A026058 A026059 A026060

Keyword

sign,easy

Author

Clark Kimberling

Extensions

New definition from Ralf Stephan, Apr 30 2004

Edited by N. J. A. Sloane, Dec 13 2008

Status

approved