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A161706 a(n) = (-11*n^5 + 145*n^4 - 635*n^3 + 1115*n^2 - 494*n + 120)/120. 21
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
{a(k): 0 <= k < 6} = divisors of 20:
a(n) = A027750(A006218(19) + k + 1), 0 <= k < A000005(20).
LINKS
Reinhard Zumkeller, Enumerations of Divisors
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
Sequence in context: A005018 A249399 A118551 * A128401 A018467 A035524
KEYWORD
sign,easy
AUTHOR
Reinhard Zumkeller, Jun 17 2009
STATUS
approved

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Last modified May 19 03:29 EDT 2024. Contains 372666 sequences. (Running on oeis4.)