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A327372 Triangle read by rows where T(n,k) is the number of unlabeled simple graphs covering n vertices with exactly k endpoints (vertices of degree 1).

%I A327372 #12 Jan 12 2024 00:50:34
%S A327372 1,0,0,0,0,1,1,0,1,0,3,1,1,1,1,11,5,4,1,2,0,62,29,18,6,4,2,1,510,225,
%T A327372 101,32,13,4,3,0,7459,2674,842,223,72,19,9,3,1,197867,50834,10784,
%U A327372 2171,504,115,34,9,4,0,9808968,1653859,228863,32322,5268,944,209,46,16,4,1
%N A327372 Triangle read by rows where T(n,k) is the number of unlabeled simple graphs covering n vertices with exactly k endpoints (vertices of degree 1).
%H A327372 Andrew Howroyd, <a href="/A327372/b327372.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50)
%H A327372 Gus Wiseman, <a href="/A327372/a327372.png">The unlabeled graphs covering 5 vertices with k endpoints.</a>
%F A327372 Column-wise first differences of A327371.
%e A327372 Triangle begins:
%e A327372    1
%e A327372    0  0
%e A327372    0  0  1
%e A327372    1  0  1  0
%e A327372    3  1  1  1  1
%e A327372   11  5  4  1  2  0
%o A327372 (PARI) \\ Needs G(n) defined in A327371.
%o A327372 T(n)={my(v=Vec(G(n)*(1 - x))); vector(#v, n, Vecrev(v[n], n))}
%o A327372 my(A=T(10)); for(n=1, #A, print(A[n])) \\ _Andrew Howroyd_, Jan 11 2024
%Y A327372 Row sums are A002494.
%Y A327372 Column k = 0 is A261919.
%Y A327372 The non-covering version is A327371.
%Y A327372 The labeled version is A327377.
%Y A327372 Cf. A000088, A004110, A294217, A327227, A327369, A327370.
%K A327372 nonn,tabl
%O A327372 0,11
%A A327372 _Gus Wiseman_, Sep 04 2019
%E A327372 Terms a(21) and beyond from _Andrew Howroyd_, Sep 11 2019