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 A138190 #32 Feb 16 2025 08:33:07
%S A138190 0,1,2,5,10,35,28,42,60,165,110,143,182,455,280,340,408,969,570,665,
%T A138190 770,1771,1012,1150,1300,2925,1638,1827,2030,4495,2480,2728,2992,6545,
%U A138190 3570,3885,4218,9139,4940,5330,5740,12341,6622,7095,7590,16215,8648
%N A138190 Numerator of (n-1)*n*(n+1)/12.
%H A138190 Colin Barker, <a href="/A138190/b138190.txt">Table of n, a(n) for n = 1..1000</a>
%H A138190 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KirchhoffIndex.html">Kirchhoff Index</a>.
%H A138190 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,4,0,0,0,-6,0,0,0,4,0,0,0,-1).
%F A138190 a(n+2) = numerator of A000295(n+2)/(3*Integral_{t=0..2} t^n*(1-abs(1-t))^2).
%F A138190 a(n) = (n*(n-1)*(n+1)*(5+((-1)^n-(-1)^((2*n-1+(-1)^n)/4)-(-1)^((6*n-1+(-1)^n)/4))))/48. - _Luce ETIENNE_, Feb 17 2015
%F A138190 G.f.: x^2*(x^12 +2*x^11 +5*x^10 +10*x^9 +31*x^8 +20*x^7 +22*x^6 +20*x^5 +31*x^4 +10*x^3 +5*x^2 +2*x +1) / ((x -1)^4*(x +1)^4*(x^2 +1)^4). - _Colin Barker_, Feb 17 2015
%F A138190 Sum_{n>=2} 1/a(n) = 3 * (1 - log(2)/2). - _Amiram Eldar_, Aug 11 2022
%e A138190 0, 1/2, 2, 5, 10, 35/2, 28, 42, 60, 165/2, 110, 143, 182, ...
%t A138190 Table[(n^3-n)/12,{n,50}]//Numerator (* or *) LinearRecurrence[{0,0,0,4,0,0,0,-6,0,0,0,4,0,0,0,-1},{0,1,2,5,10,35,28,42,60,165,110,143,182,455,280,340},50] (* _Harvey P. Dale_, Nov 05 2021 *)
%o A138190 (PARI) a(n) = numerator((n-1)*n*(n+1)/12); \\ _Michel Marcus_, Feb 17 2015
%o A138190 (PARI) a(n)=binomial(n+1,3)/if(n%4==2,1,2) \\ _Charles R Greathouse IV_, Feb 17 2015
%Y A138190 Cf. A000295, A138191.
%K A138190 nonn,frac,easy
%O A138190 1,3
%A A138190 _Eric W. Weisstein_, Mar 04 2008