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 A331504 #25 Mar 24 2020 02:53:53
%S A331504 1,1,3,20,252,6435,352716,40116600,9075135300,4116715363800,
%T A331504 3824345300380220,7219428434016265740,27217014869199032015600,
%U A331504 205397724721029574666088520,3136262529306125724764953838760
%N A331504 Number of labeled graphs with n nodes and floor(n*(n-1)/4) edges.
%C A331504 The expected number of edges of a random graph is n*(n - 1)/4. [See the Cieslik reference.]
%D A331504 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 109.
%H A331504 Dietmar Cieslik, <a href="https://math-inf.uni-greifswald.de/storages/uni-greifswald/fakultaet/mnf/mathinf/boldt/pdf-dateien/cieslik-counting-graphs.pdf">Counting Networks</a>.
%H A331504 Carlos R. Lucatero, <a href="https://www.intechopen.com/online-first/combinatorial-enumeration-of-graphs">Combinatorial Enumeration of Graphs</a>.
%F A331504 a(n) = binomial(binomial(n,2), floor(n*(n-1)/4)).
%e A331504 a(4) is 20 because for n=4, floor(n*(n-1)/4) = 3, and there are A000717(4) = 3 graphs with four points and three edges. See figure below or J. Riordan reference.
%e A331504 The non-isomorphic graphs with four nodes and three edges along with the corresponding number of labeled graphs are as follows:
%e A331504 .
%e A331504 *--* *--* *
%e A331504 | / | |
%e A331504 |/ * | |
%e A331504 * *--* *--*--*
%e A331504 4 12 4
%o A331504 (PARI) a(n) = binomial(binomial(n,2), n*(n-1)\4);
%Y A331504 Cf. A000717 ("unlabeled case"), A084546.
%K A331504 nonn
%O A331504 1,3
%A A331504 _Washington Bomfim_, Jan 18 2020