OFFSET
1,2
COMMENTS
Also, number of labeled blobs with n edges.
REFERENCES
R. C. Read, Graphical enumeration by cycle-index sums: first steps toward a unified treatment, preprint, Sept. 26, 1991.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.39, page 133, g(n).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..100
R. P. Stanley, Enumeration of posets generated by disjoint unions and ordinal sums, Proc. Amer. Math. Soc. 45 (1974), 295-299.
FORMULA
Read (1991) reference gives generating functions (see PARI code for one example).
a(n) = (n-1)!*sum(k=1..n-1, binomial(n+k-1,n-1)*sum(j=1..k, binomial(k,j)*((sum(l=0..j-1, (binomial(j,l)*((-1)^(n-l+j-1)+1)*sum(r=1..j-l, binomial(j-l,r)*2^(j-l-r-1)*(-1)^(r-j)*sum(i=0..r, (r-2*i)^(n-l+j-1)*binomial(r,i))))/(n-l+j-1)!))))), n>1, a(1)=1. - Vladimir Kruchinin, Feb 19 2012
a(n) ~ n^(n-1) / (5^(1/4)*exp(n)*(2-sqrt(5)+log((1+sqrt(5))/2))^(n-1/2)). - Vaclav Kotesovec, Mar 09 2014
MAPLE
(continue from A053554) t1 := log(1+EGF053554): t2 := series(t1, x, 30); SERIESTOLISTMULT(t2);
MATHEMATICA
Drop[ CoefficientList[ InverseSeries[ Series[x + 2*(1 - Cosh[x]) , {x, 0, 19}], y], y], 1]* Range[19]! (* Jean-François Alcover, Sep 21 2011, after g.f. *)
PROG
(PARI) /* Joerg Arndt, Feb 04 2011 */
x='x+O('x^55); t=x+2*(1-cosh(x));
Vec(serlaplace(serreverse(t))) /* show terms */
(Maxima) a(n):=if n=1 then 1 else (n-1)!*sum(binomial(n+k-1, n-1)*sum(binomial(k, j)*((sum((binomial(j, l)*((-1)^(n-l+j-1)+1)*sum(binomial(j-l, r)*2^(j-l-r-1)*(-1)^(r-j)*sum((r-2*i)^(n-l+j-1)*binomial(r, i), i, 0, r), r, 1, j-l))/(n-l+j-1)!, l, 0, j-1))), j, 1, k), k, 1, n-1); /* Vladimir Kruchinin, Feb 19 2012 */
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
N. J. A. Sloane, Dec 16 2000
EXTENSIONS
More terms from Joerg Arndt, Feb 04 2011
STATUS
approved