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%I M1939 #49 Dec 16 2020 06:20:31
%S 1,2,9,52,365,3006,28357,301064,3549177,45965530,648352001,9888877692,
%T 162112109029,2841669616982,53025262866045,1049180850990736,
%U 21937381717388657,483239096122434354,11184035897992673017
%N Exponential generating function x*exp(x/(1-x)).
%C a(n) is the number of labeled rooted trees with every non-root vertex of degree 1 or 2. - _Geoffrey Critzer_, May 21 2012.
%C Total number of unit length lists in all sets of lists, cf. A000262. - _Alois P. Heinz_, May 10 2016
%D Getu, S.; Shapiro, L. W.; Combinatorial view of the composition of functions. Ars Combin. 10 (1980), 131-145.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A006152/b006152.txt">Table of n, a(n) for n = 1..200</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=156">Encyclopedia of Combinatorial Structures 156</a>
%F a(n) = n*A000262(n-1).
%F 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
%F a(n) ~ n^(n-1/4)*exp^(2*sqrt(n)-n-1/2)/sqrt(2). - _Vaclav Kotesovec_, Oct 05 2012
%F a(n) = A320264(n+1,n). - _Alois P. Heinz_, Oct 08 2018
%t nn = 17; a = x/(1 - x);
%t Range[0, nn]! CoefficientList[Series[x Exp[a], {x, 0, nn}], x] (* _Geoffrey Critzer_, May 21 2012 *)
%o (PARI) a(n)=n!*polcoeff(x*exp(x/(1-x)+O(x^n)), n)
%Y Cf. A000262, A320264.
%K nonn,easy
%O 1,2
%A _Simon Plouffe_
%E More terms from _Michael Somos_, Jun 07 2000
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