OFFSET
0,3
COMMENTS
This is also the number of possible positions of n intervals on a line having a common non-punctual intersection. Proof: Let us denoted each interval Ai (1 <= i <= n) by the string AiAi. Then the set of all such relative positions is given by the S-language [A1 ⊗ A2 ... ⊗ An]^2. The cardinality of $A1 ⊗ A2 ... ⊗ An$ is given by A000670. - Sylviane R. Schwer (schwer(AT)lipn.univ-paris13.fr), Nov 26 2007
FORMULA
a(n) = sum(sum((k*l)^n/2^(k+l+2),k=0..infinity),l=0..infinity).
G.f.: sum(1/(2-exp(n*x))/2^(n+1),n=0..infinity).
Sum_{n>=0} a(n)*log(1+x)^n/n! = o.g.f. of A101370. [Paul D. Hanna, Nov 07 2009]
a(n) ~ (n!)^2 / (4 * (log(2))^(2*n+2)). - Vaclav Kotesovec, May 03 2015
MATHEMATICA
Table[(PolyLog[ -z, 1/2]/2)^2, {z, 1, 25}] - Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Oct 10 2006
PROG
(PARI) {a(n)=sum(k=0, n, stirling(n, k, 2)*k!)^2} \\ Paul D. Hanna, Nov 07 2009
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Sep 23 2006
EXTENSIONS
More terms from Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Oct 10 2006
STATUS
approved