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A122078 Triangle read by rows: T(n,k) is the number of unlabeled acyclic digraphs with n >= 0 nodes and n-k outnodes (0 <= k <= n).

%I A122078 #21 Jan 09 2022 12:59:17
%S A122078 1,1,0,1,1,0,1,2,3,0,1,3,11,16,0,1,4,25,108,164,0,1,5,47,422,2168,
%T A122078 3341,0,1,6,78,1251,15484,88747,138101,0,1,7,120,3124,79836,1215783,
%U A122078 7409117,11578037,0,1,8,174,6925,333004,11620961,199203464,1252610909,1961162564,0
%N A122078 Triangle read by rows: T(n,k) is the number of unlabeled acyclic digraphs with n >= 0 nodes and n-k outnodes (0 <= k <= n).
%D A122078 R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
%H A122078 Andrew Howroyd, <a href="/A122078/b122078.txt">Table of n, a(n) for n = 0..495</a> (rows 0..30; rows 0..15 from R. W. Robinson)
%H A122078 Andrew Howroyd, <a href="/A122078/a122078_1.txt">PARI program</a>, Dec 2021, updated Jan 2022.
%e A122078 Triangle T(n,k) begins:
%e A122078   1:
%e A122078   1, 0;
%e A122078   1, 1,  0;
%e A122078   1, 2,  3,    0;
%e A122078   1, 3, 11,   16,     0;
%e A122078   1, 4, 25,  108,   164,     0;
%e A122078   1, 5, 47,  422,  2168,  3341,      0;
%e A122078   1, 6, 78, 1251, 15484, 88747, 138101, 0;
%e A122078   ...
%o A122078 (PARI) \\ See link for program code.
%o A122078 { my(T=AcyclicDigraphsByNonSources(8)); for(n=1, #T, print(T[n])) } \\ _Andrew Howroyd_, Dec 31 2021
%Y A122078 Row sums give A003087.
%Y A122078 Diagonals include A000007, A350415.
%Y A122078 Cf. A058876 (labeled case), A350447, A350448, A350449, A350450.
%K A122078 nonn,tabl
%O A122078 0,8
%A A122078 _N. J. A. Sloane_, Oct 18 2006
%E A122078 Zero terms inserted by _Andrew Howroyd_, Dec 29 2021