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A006152
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Exponential generating function x*exp(x/(1-x)).
(Formerly M1939)
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8
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1, 2, 9, 52, 365, 3006, 28357, 301064, 3549177, 45965530, 648352001, 9888877692, 162112109029, 2841669616982, 53025262866045, 1049180850990736, 21937381717388657, 483239096122434354, 11184035897992673017
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OFFSET
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1,2
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COMMENTS
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a(n) is the number of labeled rooted trees with every non-root vertex of degree 1 or 2. - Geoffrey Critzer, May 21 2012.
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REFERENCES
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Getu, S.; Shapiro, L. W.; Combinatorial view of the composition of functions. Ars Combin. 10 (1980), 131-145.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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D-finite with recurrence a(n) = 2*(n-1)*a(n-1)-(n^2-5*n+5)*a(n-2)-(n-4)*(n-2)*a(n-3). - Vaclav Kotesovec, Oct 05 2012
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MATHEMATICA
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nn = 17; a = x/(1 - x);
Range[0, nn]! CoefficientList[Series[x Exp[a], {x, 0, nn}], x] (* Geoffrey Critzer, May 21 2012 *)
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PROG
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(PARI) a(n)=n!*polcoeff(x*exp(x/(1-x)+O(x^n)), n)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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