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

0,7

Comments

Row sums = A000088.

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

Column k = 0 is A002494.

Links

Table of n, a(n) for n=0..65.

Formula

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

Example

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

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

Crossrefs

Cf. A000088, A002494, A006897.

Sequence in context: A266854 A326882 A265170 * A331161 A176887 A076422

Adjacent sequences: A217650 A217651 A217652 * A217654 A217655 A217656

Keyword

nonn,tabl

Author

Geoffrey Critzer, Oct 09 2012

Status

approved