This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A161713 #27 Sep 08 2022 08:45:45
%S A161713 1,2,4,7,14,28,49,71,79,46,-70,-329,-812,-1624,-2897,-4793,-7507,
%T A161713 -11270,-16352,-23065,-31766,-42860,-56803,-74105,-95333,-121114,
%U A161713 -152138,-189161,-233008,-284576,-344837,-414841,-495719,-588686,-695044
%N A161713 a(n) = (-n^5 + 15*n^4 - 65*n^3 + 125*n^2 - 34*n + 40)/40.
%C A161713 {a(k): 0 <= k < 6} = divisors of 28:
%C A161713 a(n) = A027750(A006218(27) + k + 1), 0 <= k < A000005(28).
%H A161713 Vincenzo Librandi, <a href="/A161713/b161713.txt">Table of n, a(n) for n = 0..10000</a>
%H A161713 Reinhard Zumkeller, <a href="/A161700/a161700.txt">Enumerations of Divisors</a>
%H A161713 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A161713 a(n) = C(n,0) + C(n,1) + C(n,2) + 3*C(n,4) - 3*C(n,5).
%F A161713 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
%F A161713 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
%e A161713 Differences of divisors of 28 to compute the coefficients of their interpolating polynomial, see formula:
%e A161713 1 2 4 7 14 28
%e A161713 1 2 3 7 14
%e A161713 1 1 4 7
%e A161713 0 3 3
%e A161713 3 0
%e A161713 -3
%t A161713 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 *)
%o A161713 (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
%o A161713 (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
%o A161713 (Python)
%o A161713 def A161713(n): return n*(n*(n*(n*(15 - n) - 65) + 125) - 34)//40 + 1 # _Chai Wah Wu_, Dec 16 2021
%Y A161713 Cf. A000124, A000125, A000127, A002522, A005408, A006261, A016813, A018254, A058331, A080856, A086514, A161700, A161701, A161702, A161703, A161704, A161706, A161707, A161708, A161710, A161711, A161712, A161715, A161856.
%K A161713 sign,easy
%O A161713 0,2
%A A161713 _Reinhard Zumkeller_, Jun 17 2009