This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A122725 #27 Aug 12 2025 03:22:03
%S A122725 1,1,9,169,5625,292681,21930489,2236627849,297935847225,
%T A122725 50229268482121,10454564139438969,2632936466960600329,
%U A122725 789136169944454084025,277579719258755165321161,113238180214596650771616249,53030348046942317338336489609,28256184698070300360908567636025
%N A122725 a(n) = A000670(n)^2.
%C A122725 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
%F A122725 a(n) = Sum_{m>=0} Sum_{k>=0} ((k*m)^n/2^(k+m+2)).
%F A122725 G.f.: Sum_{n>=0} (1/(2-exp(n*x))/2^(n+1)).
%F A122725 Sum_{n>=0} a(n)*log(1+x)^n/n! = o.g.f. of A101370. - _Paul D. Hanna_, Nov 07 2009
%F A122725 a(n) ~ (n!)^2 / (4 * (log(2))^(2*n+2)). - _Vaclav Kotesovec_, May 03 2015
%p A122725 b:= proc(n, k) option remember;
%p A122725 `if`(n=0, 1, add(b(n-1, j)*j, j=k..k+1))
%p A122725 end:
%p A122725 a:= n-> b(n, 0)^2:
%p A122725 seq(a(n), n=0..16); # _Alois P. Heinz_, Aug 12 2025
%t A122725 Table[(PolyLog[ -z, 1/2]/2)^2, {z, 1, 16}] (* Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Oct 10 2006 *)
%o A122725 (PARI) {a(n)=sum(k=0, n, stirling(n, k, 2)*k!)^2} \\ _Paul D. Hanna_, Nov 07 2009
%Y A122725 Cf. A000670, A055203, A101370.
%K A122725 easy,nonn
%O A122725 0,3
%A A122725 _Vladeta Jovovic_, Sep 23 2006
%E A122725 More terms from Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Oct 10 2006