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A361455 Triangle read by rows: T(n,k) is the number of simple digraphs on labeled n nodes with k strongly connected components.

%I A361455 #10 May 04 2023 14:57:12
%S A361455 1,0,1,0,1,3,0,18,21,25,0,1606,1173,774,543,0,565080,271790,122595,
%T A361455 59830,29281,0,734774776,229224750,70500705,25349355,10110735,3781503,
%U A361455 0,3523091615568,685793359804,138122171880,35130437825,11002159455,3767987307,1138779265
%N A361455 Triangle read by rows: T(n,k) is the number of simple digraphs on labeled n nodes with k strongly connected components.
%H A361455 Andrew Howroyd, <a href="/A361455/b361455.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50).
%F A361455 T(n,k) = A361269(n,k)/2^n.
%e A361455 Triangle begins:
%e A361455   1;
%e A361455   0,         1;
%e A361455   0,         1,         3;
%e A361455   0,        18,        21,       25;
%e A361455   0,      1606,      1173,      774,      543;
%e A361455   0,    565080,    271790,   122595,    59830,    29281;
%e A361455   0, 734774776, 229224750, 70500705, 25349355, 10110735, 3781503;
%e A361455   ...
%o A361455 (PARI)
%o A361455 Z(p, f)={my(n=serprec(p, x)); serconvol(p, sum(k=0, n-1, x^k*f(k), O(x^n)))}
%o A361455 G(e, p)={Z(p, k->1/e^(k*(k-1)/2))}
%o A361455 U(e, p)={Z(p, k->e^(k*(k-1)/2))}
%o A361455 DigraphEgf(n, e)={sum(k=0, n, e^(k*(k-1))*x^k/k!, O(x*x^n) )}
%o A361455 T(n)={my(e=2); [Vecrev(p) | p<-Vec(serlaplace(U(e, 1/G(e, exp(y*log(U(e, 1/G(e, DigraphEgf(n, e)))))))))]}
%o A361455 { my(A=T(6)); for(i=1, #A, print(A[i])) }
%Y A361455 Column k=1 is A003030.
%Y A361455 Main diagonal is A003024.
%Y A361455 Row sums are A053763.
%Y A361455 The unlabeled version is A361582.
%Y A361455 Cf. A189898 (weak components), A361269 (loops allowed), A361591.
%K A361455 nonn,tabl
%O A361455 0,6
%A A361455 _Andrew Howroyd_, Mar 16 2023