# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a351287
Showing 1-1 of 1

%I A351287 #14 Feb 06 2022 22:45:36
%S A351287 1,2,4,16,84,936,16758,602544,37693734,4588585904,1016082688298,
%T A351287 436137488655846,348748058993750616,538461898813943437676
%N A351287 Number of symmetric 0-1 matrices with zero main diagonal and nondecreasing number of ones in the rows.
%C A351287 Also, number of graphs with vertices labeled 1, 2, ..., n such that their degrees are nondecreasing.
%o A351287 (Sage) def A351287(n): return sum(prod(factorial(e) for e in Partition((d+1 for d in G.degree_sequence())).to_exp()) // G.automorphism_group(return_group=False, order=True) for G in graphs(n))
%o A351287 (PARI) \\ See link in A295193 for GraphsByDegreeSeq.
%o A351287 a(n)={my(M=GraphsByDegreeSeq(n,n,(p,r)->1)); sum(i=1, matsize(M)[1], my(u=Vec(M[i,1])); prod(j=1, #u, u[j]!)*M[i,2]/n!)} \\ _Andrew Howroyd_, Feb 06 2022
%Y A351287 Cf. A016121, A351157, A351288.
%K A351287 nonn,more
%O A351287 1,2
%A A351287 _Max Alekseyev_, Feb 06 2022
%E A351287 a(11)-a(14) from _Andrew Howroyd_, Feb 06 2022

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE