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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
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.
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
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Oct 09 2012
STATUS
approved