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 A296913 #17 Dec 26 2017 03:29:07 %S A296913 0,0,120,12960,332880,3868080,27767880,144278400,594347040,2055598560, %T A296913 6202551960,16774966560,41473626480,95135323920,204803912040, %U A296913 417515696640,811858751040,1514650599360,2724410748600,4743687388320,8022734847120,13217533726320,21265702652040,33484472926080,51695588642400,78382758698400,116888127197400 %N A296913 Number of ways to properly color the Petersen graph using n colors. %H A296913 Michael De Vlieger, <a href="/A296913/b296913.txt">Table of n, a(n) for n = 1..10000</a> %H A296913 M. Baker, <a href="https://doi.org/10.1090/bull/1599">Hodge Theory in Combinatorics</a>, Bull. Amer. Math. Soc., 55 (No. 1, 2018), 57-80. See p. 60. %H A296913 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1). %F A296913 a(n) = n^10 - 15*n^9 + 105*n^8 - 455*n^7 + 1353*n^6 - 2861*n^5 + 4275*n^4 - 4305*n^3 + 2606*n^2 - 704*n. %F A296913 From _Colin Barker_, Dec 24 2017: (Start) %F A296913 G.f.: 120*x^3*(1 + 97*x + 1641*x^2 + 7495*x^3 + 11905*x^4 + 7269*x^5 + 1693*x^6 + 139*x^7) / (1 - x)^11. %F A296913 a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11. %F A296913 (End) %t A296913 Array[#^10 - 15 #^9 + 105 #^8 - 455 #^7 + 1353 #^6 - 2861 #^5 + 4275 #^4 - 4305 #^3 + 2606 #^2 - 704 # &, 27] (* _Michael De Vlieger_, Dec 23 2017 *) %t A296913 Rest@ CoefficientList[ Series[-120 x^3 (139x^7 +1693x^6 +7269x^5 +11905x^4 +7495x^3 +1641x^2 +97x +1)/(x -1)^11, {x, 0, 23}], x] (* or *) %t A296913 LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {0, 0, 120, 12960, 332880, 3868080, 27767880, 144278400, 594347040, 2055598560, 6202551960}, 23] (* _Robert G. Wilson v_, Dec 24 2017 *) %o A296913 (PARI) concat(vector(2), Vec(120*x^3*(1 + 97*x + 1641*x^2 + 7495*x^3 + 11905*x^4 + 7269*x^5 + 1693*x^6 + 139*x^7) / (1 - x)^11 + O(x^40))) \\ _Colin Barker_, Dec 24 2017 %Y A296913 Cf. A159233, A296912. %K A296913 nonn,easy %O A296913 1,3 %A A296913 _N. J. A. Sloane_, Dec 22 2017