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A136281
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Number of graphs on n labeled nodes with degree at most 2.
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6
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1, 2, 8, 41, 253, 1858, 15796, 152219, 1638323, 19467494, 252998224, 3568259503, 54263159347, 884834059454, 15397757661092, 284767413357977, 5576696746139689, 115269732256964626, 2507575465491619672, 57262481225957071721, 1369461739453440893261
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| These are thunderstorm graphs. Their connected components are a single cycle (clouds), a path (ligtning bolts) or an isolated vertex (raindrops). [Geoffrey Critzer, May 11 2011]
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REFERENCES
| D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
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FORMULA
| Binomial transform of A000986. E.g.f.: (1-x)^(-1/2)*exp(-x^2/4 + x/((2*(1-x)))). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 20 2008
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MATHEMATICA
| f = (Log[1/(1-x)]+1/(1-x) -x^2/2 - 1)/2;
Range[0, 25]! CoefficientList[Series[Exp[f], {x, 0, 25}], x] (* Geoffrey Critzer, May 11 2011 *)
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CROSSREFS
| Cf. A000085 (degree at most 1), A136282-A136286.
Sequence in context: A093935 A099240 A134055 * A125698 A052447 A153537
Adjacent sequences: A136278 A136279 A136280 * A136282 A136283 A136284
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KEYWORD
| nonn
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AUTHOR
| D. E. Knuth, Mar 31 2008
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), May 20 2008
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