A132123 a(n) = n * (2*n + 1) * (6*n^2 + 4*n + 1) / 3.

0, 11, 110, 469, 1356, 3135, 6266, 11305, 18904, 29811, 44870, 65021, 91300, 124839, 166866, 218705, 281776, 357595, 447774, 554021, 678140, 822031, 987690, 1177209, 1392776, 1636675, 1911286, 2219085, 2562644, 2944631, 3367810, 3835041

Offset: 0

Author

Reinhard Zumkeller, Aug 12 2007

Keywords

• nonn
• easy

Comments

Central terms of the triangle in A132121.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Programs

Magma

[n*(2*n+1)*(6*n^2+4*n+1)/3: n in [0..40]]; // G. C. Greubel, Mar 16 2019

Maple

seq((1/3)*n*(2*n+1)*(6*n^2+4*n+1),n=0..32); # Emeric Deutsch, Aug 19 2007

Mathematica

Table[n(2n+1)(6n^2+4n+1)/3,{n,0,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{0,11,110,469,1356},40] (* Harvey P. Dale, Jun 02 2015 *)

PARI

{a(n) = n*(2*n+1)*(6*n^2+4*n+1)/3}; \\ G. C. Greubel, Mar 16 2019

Sage

[n*(2*n+1)*(6*n^2+4*n+1)/3 for n in (0..40)] # G. C. Greubel, Mar 16 2019

Formula

G.f.: x*(11 + 55*x + 29*x^2 + x^3)/(1-x)^5. - Emeric Deutsch, Aug 19 2007

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5); a(0)=0, a(1)=11, a(2)=110, a(3)=469, a(4)=1356. - Harvey P. Dale, Jun 02 2015

E.g.f.: x*(33 + 132*x + 86*x^2 + 12*x^3)*exp(x)/3. - G. C. Greubel, Mar 16 2019