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A218334 Triangular array read by rows. T(n,k) is the number of simple labeled graphs on n nodes with no isolated nodes and exactly k components. n>=2, 1<=k<n/2. 1
1, 4, 38, 3, 728, 40, 26704, 730, 15, 1866256, 20608, 420, 251548592, 961324, 12460, 105, 66296291072, 79643424, 484624, 5040, 34496488594816, 12495365424, 27712860, 220500, 945, 35641657548953344, 3844702446464, 2619965040, 11297440, 69300, 73354596206766622208, 2341246104706784, 458476648344, 775542460, 4192650, 10395 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

Row sums are A006129.

For even n, T(n,n/2) = A001147(n) = (2n-1)!!.

Column k = 1 is A001187.

LINKS

Alois P. Heinz, Rows n = 2..50, flattened

FORMULA

E.g.f.: exp( y*log(A(x)) ) where A(x) is the e.g.f for A006129.

EXAMPLE

1;

4;

38, 3;

728, 40;

26704, 730, 15;

1866256, 20608, 420;

251548592, 961324, 12460, 105;

66296291072, 79643424, 484624, 5040;

34496488594816, 12495365424, 27712860, 220500, 945;

MATHEMATICA

nn=12; a=Sum[2^Binomial[n, 2]x^n/n!, {n, 0, nn}]; b=a/Exp[x]; f[list_]:=Select[list, #>0&]; Map[f, Drop[Range[0, nn]!CoefficientList[Series[Exp[y Log[b]], {x, 0, nn}], {x, y}], 2]]//Flatten

CROSSREFS

Sequence in context: A027461 A144991 A073237 * A121672 A020205 A265437

Adjacent sequences:  A218331 A218332 A218333 * A218335 A218336 A218337

KEYWORD

nonn,tabf

AUTHOR

Geoffrey Critzer, Oct 26 2012

STATUS

approved

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Last modified July 2 09:21 EDT 2020. Contains 335398 sequences. (Running on oeis4.)