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A143543
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Triangle read by rows: T(n,k) = number of labeled graphs on n nodes with k connected components, 1<=k<=n.
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0
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1, 1, 1, 4, 3, 1, 38, 19, 6, 1, 728, 230, 55, 10, 1, 26704, 5098, 825, 125, 15, 1, 1866256, 207536, 20818, 2275, 245, 21, 1, 251548592, 15891372, 925036, 64673, 5320, 434, 28, 1, 66296291072, 2343580752, 76321756, 3102204, 169113, 11088, 714, 36, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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FORMULA
| SUM[n,k=0..oo] g(n,k) * x^n * y^k / n! = exp( y*( F(x) - 1 ) ) = ( SUM[n=0..oo] 2^binomial(n, 2)*x^n/n! )^y, where F(x) is e.g.f. of A001187.
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EXAMPLE
| The triangle T(n,k) starts as:
n=1: 1
n=2: 1, 1
n=3: 4, 3, 1
n=4: 38, 19, 6, 1
n=5: 728, 230, 55, 10, 1
n=6: 26704, 5098, 825, 125, 15, 1
...
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MATHEMATICA
| a= Sum[2^Binomial[n, 2] x^n/n!, {n, 0, 10}];
Rest[Transpose[Table[Range[0, 10]! CoefficientList[Series[Log[a]^n/n!, {x, 0, 10}], x], {n, 1, 10}]]] // Grid (* Geoffrey Critzer, Mar 15 2011 *)
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CROSSREFS
| Cf. A001187 (first column), A006125 (row sums), A106240 (unlabeled variant).
Sequence in context: A142158 A203412 A154960 * A176863 A067017 A067018
Adjacent sequences: A143540 A143541 A143542 * A143544 A143545 A143546
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KEYWORD
| nonn,tabl
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AUTHOR
| Max Alekseyev (maxale(AT)gmail.com), Aug 23 2008
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