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 A349849 #101 Dec 12 2021 13:20:29
%S A349849 0,0,1,45,549,3755,18120,69006,220710,616554,1545435,3544915,7552611,
%T A349849 15119325,28699034,52032540,90643260,152465316,248625765,394404489,
%U A349849 610396945,923906655,1370595996,1996425530,2859913794,4034751150,5612802975,7707539151,10457928495
%N A349849 Number of transitive relations on an n-set with exactly four ordered pairs.
%H A349849 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A349849 a(n) = C(n,2) + 42*C(n,3) + 375*C(n,4) + 1450*C(n,5) + 2940*C(n,6) + 3360*C(n,7) + 1680*C(n,8).
%F A349849 a(n) = (1/24)*(n^8 - 12*n^7 + 84*n^6 - 340*n^5 + 814*n^4 - 1130*n^3 + 829*n^2 - 246*n).
%e A349849 a(2) = binomial(2,2) = 1. The only transitive relation with four ordered pairs on the 2-set {1,2} is {(1,1),(1,2),(2,1),(2,2)}.
%Y A349849 Cf. A349919, A349927, A006905.
%K A349849 nonn,easy
%O A349849 0,4
%A A349849 _Firdous Ahmad Mala_, Dec 06 2021