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A057275 Triangle T(n,k) of number of unilaterally connected digraphs on n labeled nodes and with k arcs, k=0..n*(n-1).

%I A057275 #11 Jan 19 2022 17:26:50
%S A057275 1,0,2,1,0,0,6,20,15,6,1,0,0,0,24,222,660,908,792,495,220,66,12,1,0,0,
%T A057275 0,0,120,2304,15540,52700,109545,161120,182946,167660,125945,77520,
%U A057275 38760,15504,4845,1140,190,20,1
%N A057275 Triangle T(n,k) of number of unilaterally connected digraphs on n labeled nodes and with k arcs, k=0..n*(n-1).
%H A057275 Andrew Howroyd, <a href="/A057275/b057275.txt">Table of n, a(n) for n = 1..2680</a>
%H A057275 V. Jovovic and G. Kilibarda, <a href="http://dx.doi.org/10.1016/S0012-365X(00)00112-6">Enumeration of labeled quasi-initially connected digraphs</a>, Discrete Math., 224 (2000), 151-163.
%e A057275 Triangle begins:
%e A057275   [1],
%e A057275   [0,2,1],
%e A057275   [0,0,6,20,15,6,1],
%e A057275   [0,0,0,0,24,222,660,908,792,495,220,66,12,1],
%e A057275   ...
%e A057275 The number of unilaterally connected digraphs on 3 labeled nodes is 48 = 6+20+15+6+1.
%o A057275 (PARI) \\ See A057273 for Strong.
%o A057275 Unilaterally(n, e=2)={my(u=vector(n), s=Strong(n,e)); for(n=1, #u, u[n]=vector(n, k, binomial(n,k)*s[k]*if(k==n, 1, sum(j=1, n-k, e^(k*(n-k-j))*(e^(k*j)-1)*u[n-k][j])))); vector(#u, n, vecsum(u[n]))}
%o A057275 row(n)={Vecrev(Unilaterally(n, 1+'y)[n])}
%o A057275 { for(n=1, 5, print(row(n))) } \\ _Andrew Howroyd_, Jan 19 2022
%Y A057275 Row sums give A003029.
%Y A057275 The unlabeled version is A057270.
%Y A057275 Cf. A057271, A057272, A057273, A057274, A062735.
%K A057275 nonn,tabf
%O A057275 1,3
%A A057275 _Vladeta Jovovic_, Goran Kilibarda, Sep 14 2000