OFFSET
1,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..2680 (rows 1..20)
V. Jovovic and G. Kilibarda, Enumeration of labeled quasi-initially connected digraphs, Discrete Math., 224 (2000), 151-163.
EXAMPLE
Triangle begins:
1;
0, 2, 1;
0, 0, 9, 20, 15, 6, 1;
0, 0, 0, 64, 330, 720, 914, 792, 495, 220, 66, 12, 1;
...
The number of digraphs with a source on 3 labeled nodes is the sum of the terms in row 3, i.e., 0+0+9+20+15+6+1 = 51 = A003028(3).
PROG
(PARI) \\ See A057273 for Strong.
Lambda(t, nn, e=2)={my(v=vector(1+nn)); for(n=0, nn, v[1+n] = e^(n*(n+t-1)) - sum(k=0, n-1, binomial(n, k)*e^((n-1)*(n-k))*v[1+k])); v}
Initially(n, e=2)={my(s=Strong(n, e), v=vector(n)); for(k=1, n, my(u=Lambda(k, n-k, e)); for(i=k, n, v[i] += binomial(i, k)*u[1+i-k]*s[k])); v }
row(n)={ Vecrev(Initially(n, 1+'y)[n]) }
{ for(n=1, 5, print(row(n))) } \\ Andrew Howroyd, Jan 11 2022
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Sep 14 2000
STATUS
approved