OFFSET
1,8
REFERENCES
Archer, K., Gessel, I. M., Graves, C., & Liang, X. (2020). Counting acyclic and strong digraphs by descents. Discrete Mathematics, 343(11), 112041. See Table 2.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..2680 (rows 1..20)
Kassie Archer, Ira M. Gessel, Christina Graves, and Xuming Liang, Counting acyclic and strong digraphs by descents, arXiv:1909.01550 [math.CO], 20 Mar 2020. See Table 2.
EXAMPLE
Triangle begins:
[1] 1;
[2] 0,0,1;
[3] 0,0,0,2,9,6,1;
[4] 0,0,0,0,6,84,316,492,417,212,66,12,1;
...
Number of strongly connected digraphs on 3 labeled nodes is 18 = 2+9+6+1.
PROG
(PARI)
B(nn, e=2)={my(v=vector(nn)); for(n=1, nn, v[n] = e^(n*(n-1)) - sum(k=1, n-1, binomial(n, k)*e^((n-1)*(n-k))*v[k])); v}
Strong(n, e=2)={my(u=B(n, e), v=vector(n)); v[1]=1; for(n=2, #v, v[n] = u[n] + sum(j=1, n-1, binomial(n-1, j-1)*u[n-j]*v[j])); v}
row(n)={ Vecrev(Strong(n, 1+'y)[n]) }
{ for(n=1, 5, print(row(n))) } \\ Andrew Howroyd, Jan 10 2022
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Sep 14 2000
EXTENSIONS
Terms a(46) and beyond from Andrew Howroyd, Jan 10 2022
STATUS
approved