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URL: https://oeis.org/A161713

⇱ A161713 - OEIS

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A161713
a(n) = (-n^5 + 15*n^4 - 65*n^3 + 125*n^2 - 34*n + 40)/40.
21
1, 2, 4, 7, 14, 28, 49, 71, 79, 46, -70, -329, -812, -1624, -2897, -4793, -7507, -11270, -16352, -23065, -31766, -42860, -56803, -74105, -95333, -121114, -152138, -189161, -233008, -284576, -344837, -414841, -495719, -588686, -695044
OFFSET
0,2
COMMENTS
{a(k): 0 <= k < 6} = divisors of 28:
a(n) = A027750(A006218(27) + k + 1), 0 <= k < A000005(28).
LINKS
FORMULA
a(n) = C(n,0) + C(n,1) + C(n,2) + 3*C(n,4) - 3*C(n,5).
G.f.: -(-1+4*x-7*x^2+7*x^3-7*x^4+7*x^5)/(-1+x)^6. - R. J. Mathar, Jun 18 2009
a(0)=1, a(1)=2, a(2)=4, a(3)=7, a(4)=14, a(5)=28, a(n)=6*a(n-1)- 15*a(n-2)+ 20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Harvey P. Dale, Jan 14 2014
EXAMPLE
Differences of divisors of 28 to compute the coefficients of their interpolating polynomial, see formula:
1 2 4 7 14 28
1 2 3 7 14
1 1 4 7
0 3 3
3 0
-3
MATHEMATICA
Table[(-n^5+15n^4-65n^3+125n^2-34n)/40+1, {n, 0, 40}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 2, 4, 7, 14, 28}, 40] (* Harvey P. Dale, Jan 14 2014 *)
PROG
(Magma) [(-n^5 + 15*n^4 - 65*n^3 + 125*n^2 - 34*n + 40)/40: n in [0..40]]; // Vincenzo Librandi, Jul 17 2011
(PARI) a(n)=(-n^5+15*n^4-65*n^3+125*n^2-34*n+40)/40 \\ Charles R Greathouse IV, Sep 24 2015
(Python)
def A161713(n): return n*(n*(n*(n*(15 - n) - 65) + 125) - 34)//40 + 1 # Chai Wah Wu, Dec 16 2021
KEYWORD
sign,easy
AUTHOR
Reinhard Zumkeller, Jun 17 2009
STATUS
approved