A370065 Triangle read by rows: T(n,k) is the number of simple graphs on n labeled nodes with k articulation vertices, (0 <= k <= n).
1, 1, 0, 2, 0, 0, 5, 3, 0, 0, 24, 28, 12, 0, 0, 334, 390, 240, 60, 0, 0, 13262, 10776, 6090, 2280, 360, 0, 0, 1106862, 615860, 255570, 92820, 23520, 2520, 0, 0, 175376048, 66625504, 19275424, 5446560, 1429680, 262080, 20160, 0, 0, 52257938968, 13210716600, 2592577512, 520122456, 112145040, 22649760, 3144960, 181440, 0, 0
Offset: 0
Examples
Triangle begins:
1;
1, 0;
2, 0, 0;
5, 3, 0, 0;
24, 28, 12, 0, 0;
334, 390, 240, 60, 0, 0;
13262, 10776, 6090, 2280, 360, 0, 0;
1106862, 615860, 255570, 92820, 23520, 2520, 0, 0;
...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
- S. Selkow, The enumeration of labeled graphs by number of cutpoints, Discr. Math. 185 (1998), 183-191.
Programs
-
PARI
\\ Needs G, J defined in A370064. T(n)={my(v=Vec( ((y-1)*x + serreverse(x/((1-y) + y*exp(G(n)))))/y ), w=Vec(serlaplace(exp(sum(k=1, n, Polrev(J(v[k],k),y)*x^k, O(x*x^n)) )))); vector(#w, n, Vecrev(w[n],n))} { my(A=T(8)); for(i=1, #A, print(A[i])) }