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 A351287 Number of symmetric 0-1 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also, number of graphs with vertices labeled 1, 2, ..., n such that their degrees are nondecreasing. LINKS Table of n, a(n) for n=1..14. 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), my(u=Vec(M[i, 1])); prod(j=1, #u, u[j]!)*M[i, 2]/n!)} \\ Andrew Howroyd, Feb 06 2022 CROSSREFS Cf. A016121, A351157, A351288. Sequence in context: A295922 A300100 A212432 * A013115 A291286 A007171 Adjacent sequences: A351284 A351285 A351286 * A351288 A351289 A351290 KEYWORD nonn,more AUTHOR Max Alekseyev, Feb 06 2022 EXTENSIONS a(11)-a(14) from Andrew Howroyd, Feb 06 2022 STATUS approved

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Last modified October 1 14:54 EDT 2023. Contains 365826 sequences. (Running on oeis4.)