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 A131675 #31 Oct 04 2024 10:58:05
%S A131675 1,6,1221,231880,13443885,340203456,4910472385,47565216504,
%T A131675 342540938025,1962871989130,9382270310061,38701449021984,
%U A131675 141297910237237,465502930269300,1404867737405385,3930816255364816,10296122969028753,25448298063869070,59744930256741205
%N A131675 a(n) = (Product_{i=1..5} n^i+i)/5!.
%C A131675 See A131685 about well-definedness. - _M. F. Hasler_, May 02 2015
%H A131675 T. D. Noe, <a href="/A131675/b131675.txt">Table of n, a(n) for n = 0..1000</a>
%H A131675 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H A131675 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
%F A131675 G.f.: (135*x^14 +86852*x^13 +5864611*x^12 +109724496*x^11 +782427151*x^10 +2468818430*x^9 +3704965659*x^8 +2710222344*x^7 +952834509*x^6 +152249688*x^5 +9878785*x^4 +212504*x^3 +1245*x^2 -10*x +1) / (x -1)^16. - _Colin Barker_, Apr 24 2015
%t A131675 Table[x = 5; Product[(n^k) + k, {k, x}]/x!, {n, 0, 17}] (* _Michael De Vlieger_, Apr 24 2015 *)
%t A131675 LinearRecurrence[{16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1},{1,6,1221,231880,13443885,340203456,4910472385,47565216504,342540938025,1962871989130,9382270310061,38701449021984,141297910237237,465502930269300,1404867737405385,3930816255364816},20] (* _Harvey P. Dale_, Oct 04 2024 *)
%o A131675 (PARI) Vec((135*x^14 +86852*x^13 +5864611*x^12 +109724496*x^11 +782427151*x^10 +2468818430*x^9 +3704965659*x^8 +2710222344*x^7 +952834509*x^6 +152249688*x^5 +9878785*x^4 +212504*x^3 +1245*x^2 -10*x +1) / (x -1)^16 + O(x^100)) \\ _Colin Barker_, Apr 24 2015
%o A131675 (Magma) [((n+1)*(n^2+2)*(n^3+3)*(n^4+4)*(n^5+5))/Factorial(5): n in [0..20]]; // _Vincenzo Librandi_, Apr 25 2015
%o A131675 (PARI) A131675(n,k=5)=prod(i=1,k,(n^i+i))/k! \\ Changing the optional 2nd argument allows one to produce A000027 (k=1), A064808 (k=2), A131509 (k=3), A129995 (k=4), A131676 (k=6), ..., A131680 (k=10). - _M. F. Hasler_, May 02 2015
%K A131675 nonn,easy
%O A131675 0,2
%A A131675 _Alexander R. Povolotsky_, Sep 15 2007
%E A131675 Definition made explicit by _M. F. Hasler_, May 02 2015