A161701 a(n) = (n^5 - 5*n^4 + 5*n^3 + 5*n^2 + 114*n + 120)/120.

1, 2, 3, 4, 6, 12, 28, 64, 135, 262, 473, 804, 1300, 2016, 3018, 4384, 6205, 8586, 11647, 15524, 20370, 26356, 33672, 42528, 53155, 65806, 80757, 98308, 118784, 142536, 169942, 201408, 237369, 278290, 324667, 377028, 435934, 501980, 575796, 658048

Offset: 0

Author

Reinhard Zumkeller, Jun 17 2009

Keywords

• nonn
• easy

Comments

{a(k): 0 <= k < 6} = divisors of 12:

a(n) = A027750(A006218(11) + k + 1), 0 <= k < A000005(12).

Examples

			Differences of divisors of 12 to compute the coefficients of their interpolating polynomial, see formula:
  1     2     3     4     6    12
     1     1     1     2     6
        0     0     1     4
           0     1     3
              1     2
                 1
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• R. Zumkeller, Enumerations of Divisors
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A000124, A000125, A000127, A002522, A005408, A006261, A016813, A058331, A080856, A086514, A161702, A161703, A161704, A161706, A161707, A161708, A161710, A161711, A161712, A161713, A161715.

Programs

Magma

[(n^5 - 5*n^4 + 5*n^3 + 5*n^2 + 114*n + 120)/120: n in [0..50]]; // Vincenzo Librandi, Dec 27 2010

Maple

A161701:=n->(n^5 - 5*n^4 + 5*n^3 + 5*n^2 + 114*n + 120)/120: seq(A161701(n), n=0..60); # Wesley Ivan Hurt, Jul 16 2017

Mathematica

CoefficientList[Series[(1-4*x+6*x^2-4*x^3+2*x^4)/(1-x)^6, {x, 0, 50}], x] (* G. C. Greubel, Jul 16 2017 *)

PARI

a(n)=(n^5-5*n^4+5*n^3+5*n^2+114*n+120)/120 \\ Charles R Greathouse IV, Sep 24 2015

Formula

a(n) = C(n,0) + C(n,1) + C(n,4) + C(n,5).

G.f.: (1-4*x+6*x^2-4*x^3+2*x^4)/(1-x)^6. - Colin Barker, Aug 20 2012