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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 A350448 #6 Dec 31 2021 19:58:37
%S A350448 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 A350448 1024,0,1,163,5668,36428,83648,84992,32768,0,1,556,67926,959718,
%U A350448 3919584,7097088,6144000,2097152,0,1,2222,1137641,37205922,268989920,793138688,1175224320,880803840,268435456,0
%N 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.
%e A350448 Triangle begins:
%e A350448   1;
%e A350448   1,   0;
%e A350448   1,   1,    0;
%e A350448   1,   3,    2,     0;
%e A350448   1,   8,   14,     8,     0;
%e A350448   1,  20,   89,   128,    64,     0;
%e A350448   1,  55,  634,  1934,  2336,  1024,     0;
%e A350448   1, 163, 5668, 36428, 83648, 84992, 32768, 0;
%e A350448   ...
%o A350448 (PARI) \\ See PARI link in A122078 for program code.
%o A350448 { my(T=AcyclicDigraphsByLongestPath(8)); for(n=1, #T, print(T[n])) }
%Y A350448 Row sums are A003087.
%Y A350448 Diagonals include A000007, A006125.
%Y A350448 Cf. A122078.
%K A350448 nonn,tabl
%O A350448 0,8
%A A350448 _Andrew Howroyd_, Dec 31 2021