

A351287


Number of symmetric 01 matrices with zero main diagonal and nondecreasing number of ones in the rows.


3



1, 2, 4, 16, 84, 936, 16758, 602544, 37693734, 4588585904, 1016082688298, 436137488655846, 348748058993750616, 538461898813943437676
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OFFSET

1,2


COMMENTS

Also, number of graphs with vertices labeled 1, 2, ..., n such that their degrees are nondecreasing.


LINKS



PROG

(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))
(PARI) \\ See link in A295193 for GraphsByDegreeSeq.
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


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



