login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A122725 a(n) = A000670(n)^2. 1
1, 1, 9, 169, 5625, 292681, 21930489, 2236627849, 297935847225, 50229268482121, 10454564139438969, 2632936466960600329, 789136169944454084025, 277579719258755165321161, 113238180214596650771616249, 53030348046942317338336489609, 28256184698070300360908567636025 (list; graph; refs; listen; history; text; internal format)
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

LINKS

Table of n, a(n) for n=0..16.

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) {Stirling2(n, k)=if(k<0|k>n, 0, sum(i=0, k, (-1)^i*binomial(k, i)/k!*(k-i)^n))}

{a(n)=sum(k=0, n, Stirling2(n, k)*k!)^2} \\ Paul D. Hanna, Nov 07 2009

CROSSREFS

Cf. A101370, A055203.

Sequence in context: A202836 A052774 A276960 * A012130 A151997 A119032

Adjacent sequences:  A122722 A122723 A122724 * A122726 A122727 A122728

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 22:50 EST 2021. Contains 349590 sequences. (Running on oeis4.)