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A006152 Exponential generating function x*exp(x/(1-x)).
(Formerly M1939)
8
1, 2, 9, 52, 365, 3006, 28357, 301064, 3549177, 45965530, 648352001, 9888877692, 162112109029, 2841669616982, 53025262866045, 1049180850990736, 21937381717388657, 483239096122434354, 11184035897992673017 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n) is the number of labeled rooted trees with every non-root vertex of degree 1 or 2. - Geoffrey Critzer, May 21 2012.
Total number of unit length lists in all sets of lists, cf. A000262. - Alois P. Heinz, May 10 2016
REFERENCES
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).
LINKS
FORMULA
a(n) = n*A000262(n-1).
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
a(n) ~ n^(n-1/4)*exp^(2*sqrt(n)-n-1/2)/sqrt(2). - Vaclav Kotesovec, Oct 05 2012
a(n) = A320264(n+1,n). - Alois P. Heinz, Oct 08 2018
MATHEMATICA
nn = 17; a = x/(1 - x);
Range[0, nn]! CoefficientList[Series[x Exp[a], {x, 0, nn}], x] (* Geoffrey Critzer, May 21 2012 *)
PROG
(PARI) a(n)=n!*polcoeff(x*exp(x/(1-x)+O(x^n)), n)
CROSSREFS
Sequence in context: A305987 A355789 A231494 * A369551 A143508 A052882
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Michael Somos, Jun 07 2000
STATUS
approved

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Last modified February 22 12:59 EST 2024. Contains 370255 sequences. (Running on oeis4.)