A368569 Irregular triangle read by rows: T(n,k) is the number of essential graphs with n nodes and k (directed or undirected) edges (n >= 1, 0 <= k <= n*(n-1)/2).

1, 1, 1, 1, 3, 6, 1, 1, 6, 27, 60, 66, 24, 1, 1, 10, 75, 350, 1120, 2130, 2595, 1730, 690, 80, 1, 1, 15, 165, 1235, 6930, 27882, 79825, 162315, 236490, 245150, 180936, 91560, 29890, 5190, 240, 1

Offset

1,5

Links

Table of n, a(n) for n=1..41.

Example

Triangle T(n,k) (with n >= 1 and 0 <= k <= n*(n-1)/2) begins as follows:
  1;
  1,  1;
  1,  3,  6,   1;
  1,  6, 27,  60,   66,   24,    1;
  1, 10, 75, 350, 1120, 2130, 2595, 1730, 690, 80, 1;
  ...

Crossrefs

Row sums give A007984.

Row lengths give A000124.

Column k=1 is A000217.

Column k=2 is A239568.

Sequence in context: A104611 A076790 A095693 * A032660 A102257 A347196

Adjacent sequences: A368566 A368567 A368568 * A368570 A368571 A368572

Keyword

nonn,tabf,more

Author

Moritz Schauer, Feb 06 2024

Status

approved