A211310 - OEIS

%I #12 Oct 20 2014 17:15:15

%S 1,18,1566,354456,163932120,134973740880,180430456454640,

%T 366311352681348480

%N a(n) = number |fdw(P,(n))| of entangled P-words with s=3.

%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} (3*n)!/6^n*x^n/n! is the e.g.f. for A014606 (also the o.g.f. for A025035).

%F If true, this leads to the recurrence equation: a(n) = (3*n)!/6^n - sum {k = 1..n-1} (3*k)!/6^k*binomial(n,k)*a(n-k) with a(1) = 1.

%F (End)

%Y Cf. A014606, A025035.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Apr 08 2012