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A350793
Triangle read by rows: T(n,k) is the number of digraphs on n labeled nodes with k arcs and a global source (or sink), n >= 1, k = 0..(n-1)^2.
4
1, 0, 2, 0, 0, 9, 12, 3, 0, 0, 0, 64, 252, 396, 320, 144, 36, 4, 0, 0, 0, 0, 625, 4860, 17060, 35900, 50775, 51300, 38340, 21540, 9075, 2800, 600, 80, 5, 0, 0, 0, 0, 0, 7776, 99720, 603720, 2300310, 6206730, 12654384, 20310840, 26385240, 28273620, 25302960
OFFSET
1,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..2490 (rows 1..20)
EXAMPLE
Triangle begins:
[1] 1;
[2] 0, 2;
[3] 0, 0, 9, 12, 3;
[4] 0, 0, 0, 64, 252, 396, 320, 144, 36, 4;
...
PROG
(PARI)
InitiallyV(n, e=2)={my(v=vector(n)); for(n=1, n, v[n] = n*e^((n-1)^2) - sum(k=1, n-1, binomial(n, k)*e^((n-2)*(n-k))*v[k])); v}
row(n)={Vecrev(InitiallyV(n, 1+'y)[n])}
{ for(n=1, 5, print(row(n))) }
CROSSREFS
Row sums are A350792.
The leading diagonal is A000169.
The unlabeled version is A350797.
Sequence in context: A249387 A350487 A258759 * A181499 A010893 A181501
KEYWORD
nonn,tabf
AUTHOR
Andrew Howroyd, Jan 17 2022
STATUS
approved