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A350909
Triangle read by rows: T(n,k) is the number of weakly connected acyclic digraphs on n labeled nodes with k arcs, k=0..n*(n-1).
1
1, 0, 2, 0, 0, 12, 6, 0, 0, 0, 128, 186, 108, 24, 0, 0, 0, 0, 2000, 5640, 7840, 6540, 3330, 960, 120, 0, 0, 0, 0, 0, 41472, 189480, 456720, 730830, 832370, 690300, 416160, 178230, 51480, 9000, 720, 0, 0, 0, 0, 0, 0, 1075648, 7178640, 26035800, 65339820
OFFSET
1,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1350 (rows 1..20)
EXAMPLE
Triangle begins:
[1] 1;
[2] 0, 2;
[3] 0, 0, 12, 6;
[4] 0, 0, 0, 128, 186, 108, 24;
[5] 0, 0, 0, 0, 2000, 5640, 7840, 6540, 3330, 960, 120;
...
PROG
(PARI)
G(n)={my(v=vector(n+1)); v[1]=1; for(n=1, n, v[n+1]=sum(k=1, n, -(-1)^k*(1+y)^(k*(n-k))*v[n-k+1]/k!))/n!; Ser(v)}
row(n)={Vecrev(n!*polcoef(log(G(n)), n))}
{ for(n=1, 6, print(row(n))) }
CROSSREFS
Row sums are A082402.
Leading diagonal is A097629.
The unlabeled version is A350449.
Sequence in context: A289651 A342588 A302751 * A244139 A350732 A231031
KEYWORD
nonn,tabf
AUTHOR
Andrew Howroyd, Jan 29 2022
STATUS
approved