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 A363591 #18 Aug 30 2024 10:19:00
%S A363591 0,12,65,255,882,2870,9039,27945,85448,259512,784797,2366819,7125198,
%T A363591 21424938,64373339,193316877,580344132,1741819148,5227030665,
%U A363591 15684238119,47059006250,141189602142,423593972775,1270832250545,3812597415552,11437993573920,34314383375669
%N A363591 a(n) = 3*(3^(n-1) - 2^n + 1)/2 - binomial(n,2), n >= 3.
%C A363591 2*a(n) is the number of ordered set partitions of an n-set into 3 nonempty sets such that the number of elements in the first two sets (in total) is at least three.
%H A363591 Paolo Xausa, <a href="/A363591/b363591.txt">Table of n, a(n) for n = 3..1000</a>
%H A363591 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (8,-24,34,-23,6).
%F A363591 G.f.: x^4*(12 - 31*x + 23*x^2 - 6*x^3)/((1 - x)^3*(1 - 2*x)*(1 - 3*x)). - _Stefano Spezia_, Jun 11 2023
%e A363591 2*a(5)=130 subtracting the 20 ordered set partitions of the type {1},{2},{3,4,5} from the 150 ordered set partitions of a 5-set into 3 parts.
%t A363591 LinearRecurrence[{8, -24, 34, -23, 6}, {0, 12, 65, 255, 882}, 30] (* or *)
%t A363591 A363591[n_] := (3^n - 3*2^n - n^2 + n + 3)/2;
%t A363591 Array[A363591, 30, 3] (* _Paolo Xausa_, Aug 30 2024 *)
%Y A363591 Cf. A001117, A363603.
%K A363591 nonn,easy
%O A363591 3,2
%A A363591 _Enrique Navarrete_, Jun 10 2023