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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). 2

%I

%S 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 0,0,120,2304,15540,52700,109545,161120,182946,167660,125945,77520,

%U 38760,15504,4845,1140,190,20,1

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

%H Andrew Howroyd, <a href="/A057275/b057275.txt">Table of n, a(n) for n = 1..2680</a>

%H 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 Triangle begins:

%e [1],

%e [0,2,1],

%e [0,0,6,20,15,6,1],

%e [0,0,0,0,24,222,660,908,792,495,220,66,12,1],

%e ...

%e The number of unilaterally connected digraphs on 3 labeled nodes is 48 = 6+20+15+6+1.

%o (PARI) \\ See A057273 for Strong.

%o 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 row(n)={Vecrev(Unilaterally(n, 1+'y)[n])}

%o { for(n=1, 5, print(row(n))) } \\ _Andrew Howroyd_, Jan 19 2022

%Y Row sums give A003029.

%Y The unlabeled version is A057270.

%Y Cf. A057271, A057272, A057273, A057274, A062735.

%K nonn,tabf,changed

%O 1,3

%A _Vladeta Jovovic_, Goran Kilibarda, Sep 14 2000

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)