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 A373134 #6 Jun 22 2024 16:10:11
%S A373134 0,0,0,0,12,60,300,1260,5096,19656,73800,270600,974292,3454308,
%T A373134 12090260,41850900,143489040,487862736,1646537040,5520741840,
%U A373134 18402473180,61018726860,201361799100,661617339900,2165293112952,7060738411800,22947399839000,74349575478360,240206320776996,773998144725876
%N A373134 Expansion of e.g.f. (1/2)*(x^2*exp(x))*(sinh(x))^2.
%C A373134 a(n) is the number of ordered set partitions of an n-set into 3 sets such that the first and second sets have an odd number of elements, and two elements are selected from the third.
%F A373134 a(n) = binomial(n,2)*(3^(n-2) + (-1)^n - 2)/4.
%e A373134 For n = 6, we have the following cases:
%e A373134 {1}, {2}, {(3), (4), 5, 6} (90 of these),
%e A373134 {2}, {1}, {(3), (4), 5, 6} (90 of these),
%e A373134 {1, 2, 3}, {4}, {(5), (6)} (60 of these),
%e A373134 {1}, {2, 3, 4}, {(5), (6)} (60 of these),
%e A373134 where the two elements selected from the third set are in parentheses.
%Y A373134 Cf. A360036, A373065
%K A373134 nonn
%O A373134 0,5
%A A373134 _Enrique Navarrete_, May 26 2024