|
| |
|
|
A138013
|
|
E.g.f. satisfies: A(x) = 1 - log(1 - x*A(x)).
|
|
2
| |
|
|
1, 1, 3, 17, 146, 1694, 24834, 440586, 9180800, 219829536, 5948287560, 179508872520, 5978006444112, 217772950035120, 8614798644364080, 367768502385434640, 16852524904388586240, 825075552824125305600
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| a(n) = A038037(n+1)/(n+1) for n>=0 where A038037(n) is the number of labeled rooted compound windmills (mobiles) with n nodes.
|
|
|
FORMULA
| E.g.f.: A(x) = (1/x)*Series_Reversion[ x/(1 - log(1-x)) ].
E.g.f.: A(x) = 1 + Series_Reversion( (1-exp(-x))/(1+x) ).
E.g.f. A(x) satisfies: exp(1 - A(x)) = 1 - x*A(x).
|
|
|
EXAMPLE
| E.g.f.: A(x) = 1 + x + 3x^2/2! + 17x^3/3! + 146x^4/4! + 1694x^5/5! + ...
where A(x) = 1 - log(1 - x*A(x)):
A(x) = 1 + x*A(x) + x^2*A(x)^2/2 + x^3*A(x)^3/3 +...+ x^n*A(x)^n/n +...
|
|
|
PROG
| (PARI) {a(n)=n!*polcoeff(1/x*serreverse(x/(1-log(1-x + x*O(x^n) ))), n+1)}
(PARI) {a(n)=n!*polcoeff(1 + serreverse((1-exp(-x+x^2*O(x^n)))/(1+x +x*O(x^n))), n)}
|
|
|
CROSSREFS
| Cf. A038037.
Sequence in context: A162650 A015735 A140983 * A052807 A080253 A009813
Adjacent sequences: A138010 A138011 A138012 * A138014 A138015 A138016
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Feb 27 2008
|
| |
|
|
