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A006959 Number of labeled M-type rooted trees on n nodes.
(Formerly M4274)
1
1, 6, 65, 1092, 25272, 749034, 27108440, 1159194472, 57190952440, 3197759266112, 199831490658912, 13802087001056704, 1044075809166477232, 85847947926743165952, 7623428923066363040672, 727116625218755662644416 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
F. Bergeron, G. Labelle and P. Leroux, Théorie des espèces et Combinatoire des Structures Arborescentes, Publications du LACIM, Université du Québec à Montréal, 1994, p. 214.
F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, pp. 210, 242 (3.2.68, 3.3.92)
G. Labelle, Some new computational methods in the theory of species, pp. 192-209 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
FORMULA
E.g.f. satisfies 2*A(x) = exp(x+A(x)) - 1 - log(1-x)*A(x).
a(n) ~ n^(n-1) * sqrt(1 + (1+log(1-r))/((1-r)*(2+log(1-r))^2)) / (exp(n) * r^(n-1/2)), where r = 0.1520268451233936874315... is the root of the equation 2 + log(1-r) = exp(1+r-1/(2+log(1-r))). - Vaclav Kotesovec, Jan 08 2014
MATHEMATICA
max = 16; f[x_] := -1/(2+Log[1-x]) - ProductLog[-E^(x - 1/(2+Log[1-x]))/(2+Log[1-x])]; Rest[ CoefficientList[ Series[ f[x], {x, 0, max}], x]*Range[0, max]!](* Jean-François Alcover, Mar 07 2012, after e.g.f. *)
PROG
(PARI) {a(n) = local(A); if( n<1, 0, A = 0; for( k=1, n, A += x * O(x^k); A = truncate( exp( x + A) - 1 - A*(1 + log( 1 - x + A - A)) )); n! * polcoeff( A, n))} /* Michael Somos, Jun 07 2012 */
CROSSREFS
Cf. A052315.
Sequence in context: A243698 A217899 A349524 * A121017 A239998 A278841
KEYWORD
nonn,eigen,nice
AUTHOR
EXTENSIONS
More terms, formula from Christian G. Bower, Dec 15 1999
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)