A217653 Triangular array read by rows: T(n,k) is the number of unlabeled simple graphs with n nodes that have exactly k isolated nodes, (n>=0, 0<=k<=n).

1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 7, 2, 1, 0, 1, 23, 7, 2, 1, 0, 1, 122, 23, 7, 2, 1, 0, 1, 888, 122, 23, 7, 2, 1, 0, 1, 11302, 888, 122, 23, 7, 2, 1, 0, 1, 262322, 11302, 888, 122, 23, 7, 2, 1, 0, 1, 11730500, 262322, 11302, 888, 122, 23, 7, 2, 1, 0, 1

Offset: 0

Author

Geoffrey Critzer, Oct 09 2012

Keywords

• nonn
• tabl

Comments

Row sums = A000088.

Sum_{k=1..n} T(n,k)*k = A006897(n).

Column k = 0 is A002494.

Examples

			1,
0, 1,
1, 0, 1,
2, 1, 0, 1,
7, 2, 1, 0, 1,
23, 7, 2, 1, 0, 1,
122, 23, 7, 2, 1, 0, 1
		

Crossrefs

Cf. A000088, A002494, A006897.

Programs

Mathematica

Needs["Combinatorica`"]; nn=10; s=Sum[NumberOfGraphs[n]x^n, {n,0,nn}]; CoefficientList[Series[s (1-x)/(1-y x), {x,0,nn}], {x,y}] //Grid

Formula

O.g.f.: A(x)/(1-y*x) where A(x) is o.g.f. for A002494.