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

Author

Max Alekseyev, Feb 06 2022

Keywords

• nonn
• more

Comments

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

Crossrefs

Cf. A016121, A351157, A351288.

Programs

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

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))

Extensions

a(11)-a(14) from Andrew Howroyd, Feb 06 2022