A054547 - OEIS

%I #16 Jan 29 2022 12:16:03

%S 0,0,2,1,0,0,12,20,15,6,1,0,0,12,140,435,768,920,792,495,220,66,12,1,

%T 0,0,0,240,2520,11604,34150,73560,123495,166860,184426,167900,125965,

%U 77520,38760,15504,4845,1140,190,20,1

%N Triangular array giving number of labeled digraphs on n unisolated nodes and k=0..n*(n-1) arcs.

%H Andrew Howroyd, <a href="/A054547/b054547.txt">Table of n, a(n) for n = 1..2680</a> (rows 1..20)

%F T(n, k) = Sum_{i=0..n} (-1)^(n-i)*binomial(n, i)*binomial(i*(i-1), k).

%e Triangle T(n,k) begins:

%e   [0],

%e   [0,2,1],

%e   [0,0,12,20,15,6,1],

%e   [0,0,12,140,435,768,920,792,495,220,66,12,1],

%e   ...

%o (PARI) row(n) = {Vecrev(sum(i=0, n, (-1)^(n-i)*binomial(n,i)*(1 + 'y)^(i*(i-1))), n*(n-1)+1)}

%o { for(n=1, 6, print(row(n))) } \\ _Andrew Howroyd_, Jan 28 2022

%Y Row sums are A054545.

%Y Column sums are A121252.

%Y The unlabeled version is A350908.

%Y Cf. A054548 (graphs), A062735, A123554.

%K easy,nonn,tabf

%O 1,3

%A _Vladeta Jovovic_, Apr 09 2000