A035081 Number of increasing asymmetric rooted connected graphs where every block is a complete graph.

1, 1, 1, 7, 27, 167, 1451, 12672, 133356, 1573608, 20731512, 299642958, 4732486932, 81201040470, 1500094187292, 29730606352920, 628968809015766, 14147458062941100, 337143091156288002, 8485143902146640124

Offset: 1

Author

Christian G. Bower, Nov 15 1998

Keywords

• nonn
• eigen

Comments

In an increasing rooted graph nodes are numbered and numbers increase as you move away from root.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100
• C. G. Bower, Transforms (2)

Crossrefs

Cf. A007549, A007561, A035079, A035080.

Programs

PARI

EGJ(v)={Vec(serlaplace(prod(k=1, #v, (1 + x^k/k! + O(x*x^#v))^v[k]))-1, -#v)}
seq(n)={my(v=[1]); for(n=2, n, v=concat([1], EGJ(EGJ(v)))); v} \\ Andrew Howroyd, Sep 11 2018

Formula

Shifts left when EGJ transform applied twice.