A351287 - OEIS

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A351287

Number of symmetric 0-1 matrices with zero main diagonal and nondecreasing number of ones in the rows.

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)[1], 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