A350448 Triangle read by rows: T(n,k) is the number of acyclic graphs on n unlabeled nodes whose longest directed path has k arcs.

1, 1, 0, 1, 1, 0, 1, 3, 2, 0, 1, 8, 14, 8, 0, 1, 20, 89, 128, 64, 0, 1, 55, 634, 1934, 2336, 1024, 0, 1, 163, 5668, 36428, 83648, 84992, 32768, 0, 1, 556, 67926, 959718, 3919584, 7097088, 6144000, 2097152, 0, 1, 2222, 1137641, 37205922, 268989920, 793138688, 1175224320, 880803840, 268435456, 0

Offset: 0

Author

Andrew Howroyd, Dec 31 2021

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  1;
  1,   0;
  1,   1,    0;
  1,   3,    2,     0;
  1,   8,   14,     8,     0;
  1,  20,   89,   128,    64,     0;
  1,  55,  634,  1934,  2336,  1024,     0;
  1, 163, 5668, 36428, 83648, 84992, 32768, 0;
  ...
		

Crossrefs

Row sums are A003087.

Diagonals include A000007, A006125.

Cf. A122078.

Programs

PARI

\\ See PARI link in A122078 for program code.
{ my(T=AcyclicDigraphsByLongestPath(8)); for(n=1, #T, print(T[n])) }