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A350731 Triangle read by rows: T(n,k) is the number of strongly connected oriented graphs on n labeled nodes with k arcs, n >= 1, k=0..n*(n-1)/2.

%I A350731 #11 Jan 16 2022 17:46:09
%S A350731 1,0,0,0,0,0,2,0,0,0,0,6,36,24,0,0,0,0,0,24,480,1940,2970,2040,544,0,
%T A350731 0,0,0,0,0,120,5040,51330,221910,527940,772080,722250,426420,146160,
%U A350731 22320,0,0,0,0,0,0,0,720,52920,1026060,8810970,43268442,138984510
%N A350731 Triangle read by rows: T(n,k) is the number of strongly connected oriented graphs on n labeled nodes with k arcs, n >= 1, k=0..n*(n-1)/2.
%H A350731 Andrew Howroyd, <a href="/A350731/b350731.txt">Table of n, a(n) for n = 1..1350</a> (rows 1..20)
%e A350731 Triangle begins:
%e A350731   [1] 1;
%e A350731   [2] 0, 0;
%e A350731   [3] 0, 0, 0, 2;
%e A350731   [4] 0, 0, 0, 0, 6, 36,  24;
%e A350731   [5] 0, 0, 0, 0, 0, 24, 480, 1940, 2970, 2040, 544;
%e A350731   ...
%o A350731 (PARI)
%o A350731 OrientedGgf(n, y=1) = {sum(k=0, n, ((1+2*y)/(1+y))^(k*(k-1)/2)*x^k/k!, O(x*x^n) )}
%o A350731 StrongO(n, y=1) = {my(g=serconvol(1/OrientedGgf(n,y), sum(k=0, n, x^k*(1+y)^(k*(k-1)/2), O(x*x^n)))); Vec(serlaplace(-log(g)))}
%o A350731 row(n)={Vecrev(StrongO(n,'y)[n], n*(n-1)/2+1)}
%o A350731 { for(n=1, 6, print(row(n))) }
%Y A350731 Row sums are A350730.
%Y A350731 The unlabeled version is A350750.
%Y A350731 Cf. A057273 (digraphs), A350732 (weakly connected).
%K A350731 nonn,tabf
%O A350731 1,7
%A A350731 _Andrew Howroyd_, Jan 11 2022