A350448 - OEIS

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.

%I #6 Dec 31 2021 19:58:37

%S 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,

%T 1024,0,1,163,5668,36428,83648,84992,32768,0,1,556,67926,959718,

%U 3919584,7097088,6144000,2097152,0,1,2222,1137641,37205922,268989920,793138688,1175224320,880803840,268435456,0

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

%e Triangle begins:

%e 1;

%e 1, 0;

%e 1, 1, 0;

%e 1, 3, 2, 0;

%e 1, 8, 14, 8, 0;

%e 1, 20, 89, 128, 64, 0;

%e 1, 55, 634, 1934, 2336, 1024, 0;

%e 1, 163, 5668, 36428, 83648, 84992, 32768, 0;

%e ...

%o (PARI) \\ See PARI link in A122078 for program code.

%o { my(T=AcyclicDigraphsByLongestPath(8)); for(n=1, #T, print(T[n])) }

%Y Row sums are A003087.

%Y Diagonals include A000007, A006125.

%Y Cf. A122078.

%K nonn,tabl

%O 0,8

%A _Andrew Howroyd_, Dec 31 2021