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

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