A161706 a(n) = (-11*n^5 + 145*n^4 - 635*n^3 + 1115*n^2 - 494*n + 120)/120.

1, 2, 4, 5, 10, 20, 21, -27, -201, -626, -1486, -3035, -5608, -9632, -15637, -24267, -36291, -52614, -74288, -102523, -138698, -184372, -241295, -311419, -396909, -500154, -623778, -770651, -943900, -1146920, -1383385, -1657259, -1972807

Offset

0,2

Comments

{a(k): 0 <= k < 6} = divisors of 20:

a(n) = A027750(A006218(19) + k + 1), 0 <= k < A000005(20).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Reinhard Zumkeller, Enumerations of Divisors

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(n) = C(n,0) + C(n,1) + C(n,2) - 2*C(n,3) + 7*C(n,4) - 11*C(n,5).

G.f.: (1-4*x+7*x^2-9*x^3+15*x^4-21*x^5)/(1-x)^6. - Colin Barker, Apr 25 2012

Example

Differences of divisors of 20 to compute the coefficients of their interpolating polynomial, see formula:
  1     2     4     5    10    20
     1     2     1     5    10
        1    -1     4     5
          -2     5     1
              7    -4
               -11

Maple

A161706:=n->(-11*n^5 + 145*n^4 - 635*n^3 + 1115*n^2 - 494*n + 120)/120: seq(A161706(n), n=0..50); # Wesley Ivan Hurt, Jul 16 2017

Mathematica

CoefficientList[Series[(1 - 4*x + 7*x^2 - 9*x^3 + 15*x^4 - 21*x^5)/(1 - x)^6, {x, 0, 50}], x] (* G. C. Greubel, Jul 16 2017 *)

Prog

(Magma) [(-11*n^5 + 145*n^4 - 635*n^3 + 1115*n^2 - 494*n + 120)/120: n in [0..50]]; // Vincenzo Librandi, Dec 27 2010
(PARI) a(n)=(-11*n^5+145*n^4-635*n^3+1115*n^2-494*n+120)/120 \\ Charles R Greathouse IV, Sep 24 2015
(Python)
def A161706(n): return (n*(n*(n*(n*(145 - 11*n) - 635) + 1115) - 494) + 120)//15>>3 # Chai Wah Wu, Oct 23 2023

Crossrefs

Cf. A005408, A000124, A016813, A086514, A000125, A058331, A002522, A161701, A161702, A161703, A000127, A161704, A161707, A161708, A161710, A080856, A161711, A161712, A161713, A161715, A006261.

Cf. A005018, A161700, A161856. - Reinhard Zumkeller, Jun 21 2009

Sequence in context: A005018 A249399 A118551 * A128401 A018467 A035524

Adjacent sequences: A161703 A161704 A161705 * A161707 A161708 A161709

Keyword

sign,easy

Author

Reinhard Zumkeller, Jun 17 2009

Status

approved