|
%I #11 Oct 20 2014 17:15:15
%S 1,4,60,1776,84720,5876640,556466400,68882446080
%N a(n) = number |fdw(P,(n))| of entangled P-words with s=2.
%C See Jenca and Sarkoci for the precise definition.
%H Gejza Jenca and Peter Sarkoci, <a href="http://arxiv.org/abs/1112.5782">Linear extensions and order-preserving poset partitions</a>, arXiv preprint arXiv:1112.5782, 2011
%F From Peter Bala, Sep 05 2012: (Start)
%F Conjectural e.g.f.: 2 - 1/A(x), where A(x) = sum {n = 0..inf} (2*n)!/2^n*x^n/n! is the e.g.f. for A000680 (also the o.g.f. for A001147).
%F If true, this gives a(n) = n!*A000698(n) and leads to the recurrence equation: a(n) = (2*n)!/2^n - sum {k = 1..n-1} (2*k)!/2^k*binomial(n,k)*a(n-k) with a(1) = 1.
%F (End)
%Y Cf. A000680, A000698, A001147.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Apr 08 2012
| 