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 A168627 #18 Nov 21 2024 13:04:30
%S A168627 0,1,1056,88938,2099200,24421875,181421856,988722196,4295098368,
%T A168627 15690795525,50000500000,142656721086,371505678336,896082610423,
%U A168627 2024786349600,4324883625000,8796101410816,17135960222601
%N A168627 a(n) = n^6*(n^5 + 1)/2.
%C A168627 Number of unoriented rows of length 11 using up to n colors. For a(0)=0, there are no rows using no colors. For a(1)=1, there is one row using that one color for all positions. For a(2)=1056, there are 2^11=2048 oriented arrangements of two colors. Of these, 2^6=64 are achiral. That leaves (2048-64)/2=992 chiral pairs. Adding achiral and chiral, we get 1056. - _Robert A. Russell_, Nov 13 2018
%H A168627 G. C. Greubel, <a href="/A168627/b168627.txt">Table of n, a(n) for n = 0..1000</a>
%H A168627 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).
%F A168627 From _G. C. Greubel_, Jul 27 2016: (Start)
%F A168627 G.f.: x*(1 + 1044*x + 76332*x^2 + 1101420*x^3 + 4869558*x^4 + 7862124*x^5 + 4868556*x^6 + 1102068*x^7 + 76305*x^8 + 992*x^9)/(1 - x)^12.
%F A168627 E.g.f.: (1/2)* x *(2 + 1054*x + 28591*x^2 + 145815*x^3 + 246745*x^4 + 179488*x^5 + 63987*x^6 + 11880*x^7 + 1155*x^8 + 55*x^9 + x^10)*exp(x). (End)
%F A168627 From _Robert A. Russell_, Nov 13 2018: (Start)
%F A168627 a(n) = (A008455(n) + A001014(n)) / 2 = (n^11 + n^6) / 2.
%F A168627 G.f.: (Sum_{j=1..11} S2(11,j)*j!*x^j/(1-x)^(j+1) + Sum_{j=1..6} S2(6,j)*j!*x^j/(1-x)^(j+1)) / 2, where S2 is the Stirling subset number A008277.
%F A168627 G.f.: x*Sum_{k=0..10} A145882(11,k) * x^k / (1-x)^12.
%F A168627 E.g.f.: (Sum_{k=1..11} S2(11,k)*x^k + Sum_{k=1..6} S2(6,k)*x^k) * exp(x) / 2, where S2 is the Stirling subset number A008277.
%F A168627 For n>11, a(n) = Sum_{j=1..12} -binomial(j-13,j) * a(n-j). (End)
%t A168627 Table[n^6*(n^5+1)/2, {n, 0, 30}] (* _G. C. Greubel_, Jul 27 2016 *)
%t A168627 LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1},{0,1,1056,88938,2099200,24421875,181421856,988722196,4295098368,15690795525,50000500000,142656721086},20] (* _Harvey P. Dale_, Nov 21 2024 *)
%o A168627 (PARI) vector(30, n, n--; n^6*(1 + n^5)/2) \\ _G. C. Greubel_, Nov 15 2018
%o A168627 (Magma) [n^6*(1 + n^5)/2: n in [0..30]]; // _G. C. Greubel_, Nov 15 2018
%o A168627 (Sage) [n^6*(1 + n^5)/2 for n in range(30)] # _G. C. Greubel_, Nov 15 2018
%o A168627 (GAP) List([0..30], n -> n^6*(1 + n^5)/2); # _G. C. Greubel_, Nov 15 2018
%Y A168627 Row 11 of A277504.
%Y A168627 Cf. A008455 (oriented), A001014 (achiral).
%K A168627 nonn
%O A168627 0,3
%A A168627 _N. J. A. Sloane_, Dec 11 2009