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A060311
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E.g.f.: exp((exp(x)-1)^2/2).
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1
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1, 0, 1, 3, 10, 45, 241, 1428, 9325, 67035, 524926, 4429953, 40010785, 384853560, 3925008361, 42270555603, 478998800290, 5693742545445, 70804642315921, 918928774274028, 12419848913448565, 174467677050577515
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| After the first term, this is the Stirling transform of the sequence of moments of the standard normal (or "Gaussian") probability distribution. It is not itself a moment sequence of any probability distribution. - Michael Hardy (hardy(AT)math.umn.edu), May 29 2005
a(n) is the number of simple labeled graphs on n nodes in which each component is a complete bipartite graph. - Geoffrey Critzer, Dec 03 2011
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REFERENCES
| I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,100
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FORMULA
| E.g.f. A(x) = B(exp(x)-1) where B(x)=exp(x^2/2) is e.g.f. of A001147(2n), hence a(n) is the Stirling transform of A001147(2n). - Michael Somos Jun 01 2005
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MATHEMATICA
| a = Exp[x] - 1; Range[0, 20]! CoefficientList[Series[a^2/2, {x, 0, 20}], x] (* Geoffrey Critzer, Dec 03 2011 *)
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PROG
| (PARI) a(n)=if(n<0, 0, n!*polcoeff( exp((exp(x+x*O(x^n))-1)^2/2), n)) /* Michael Somos Jun 01 2005 */
(PARI) { for (n=0, 100, write("b060311.txt", n, " ", n!*polcoeff(exp((exp(x + x*O(x^n)) - 1)^2/2), n)); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 03 2009]
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CROSSREFS
| Sequence in context: A096752 A134018 A028417 * A184947 A099237 A006220
Adjacent sequences: A060308 A060309 A060310 * A060312 A060313 A060314
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KEYWORD
| nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 27 2001
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