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 A377464 #8 Nov 01 2024 09:36:14
%S A377464 0,0,2,12,62,290,1292,5579,23606,98490,406862,1668689,6807704,
%T A377464 27663441,112076057,453031502,1828018406,7366128866,29650536878,
%U A377464 119249689265,479277846962,1925216817095,7729973578307,31025341749680,124486445913728,499362094315865
%N A377464 Number of connected pairs of subsets of [n] with each being a different size.
%C A377464 Empirically, a(A075930(n)) == 1 (mod 2).
%F A377464 a(n) = Sum_{i=0..n-2} binomial(n,i) * Sum_{j=i+1..n-1} (binomial(n,j) - binomial(i,n-j)).
%e A377464 a(3) = 12 counts the pairs: {{1,2},{1}}, {{1,2},{2}}, {{1,3},{1}}, {{1,3},{3}}, {{2,3},{2}}, {{2,3},{3}}, {{1,2,3},{1,2}}, {{1,2,3},{1,3}}, {{1,2,3},{2,3}}, {{1,2,3},{1}}, {{1,2,3},{2}}, {{1,2,3},{3}}.
%o A377464 (PARI)
%o A377464 A377464(n) = {sum(i=0,n-2,binomial(n,i)*sum(j=i+1,n-1, binomial(n,j)-binomial(i,n-j)))}
%Y A377464 Cf. A001187, A075930, A323818, A326749.
%K A377464 nonn,easy
%O A377464 0,3
%A A377464 _John Tyler Rascoe_, Oct 29 2024