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%I #58 Feb 13 2024 09:33:51
%S 1,1,3,14,83,570,4318,35068,299907,2668994,24513578,230981316,
%T 2222973742,21777680644,216603095388,2182653550712,22245324259811,
%U 228995136248850,2378208988952434,24893925007653748,262424206657706682,2784074166633171596,29707452318776988260,318664451642694840264
%N Matchings avoiding the pattern 231.
%H Vincenzo Librandi, <a href="/A220910/b220910.txt">Table of n, a(n) for n = 0..200</a>
%H Jonathan Bloom and Sergi Elizalde, <a href="http://arxiv.org/abs/1211.3442">Pattern avoidance in matchings and partitions</a>, arXiv preprint arXiv:1211.3442 [math.CO], 2012.
%H Matteo Cervetti and Luca Ferrari, <a href="https://arxiv.org/abs/2009.01024">Pattern avoidance in the matching pattern poset</a>, arXiv:2009.01024 [math.CO], 2020.
%H W. Mlotkowski, K. A. Penson, <a href="http://arxiv.org/abs/1507.07312">A Fuss-type family of positive definite sequences</a>, arXiv:1507.07312 [math.PR], 2015, Proposition 4.4.
%H Noam Zeilberger and Alain Giorgetti, <a href="http://arxiv.org/abs/1408.5028">A correspondence between rooted planar maps and normal planar lambda terms</a>, Logical Methods in Computer Science, vol. 11 (3:22), 2015, pp. 1-39.
%F G.f.: 54*z/(1+36*z-(1-12*z)^(3/2)) [Cervetti-Ferrari]. - _N. J. A. Sloane_, Nov 30 2020
%F Special values of the hypergeometric function 2F1, in Maple notation: a(n) = (27/8)*doublefactorial(2*n-1)*6^n*hypergeom([2, n+1/2], [n+3], -3)/(n+2)!, n>0. - _Karol A. Penson_ and Wojciech Mlotkowski, Aug 04 2013
%F D-finite with recurrence n*a(n) +2*(-4*n+17)*a(n-1) +24*(-2*n+3)*a(n-2)=0. - _R. J. Mathar_, Aug 04 2013
%F G.f.: ((1-12*x)^(3/2) + (1+36*x)) / (2*(4*x+1)^2). - _Vaclav Kotesovec_, Aug 23 2014
%F a(n) ~ 2^(2*n-7) * 3^(n+3) / (sqrt(Pi) * n^(5/2)). - _Vaclav Kotesovec_, Aug 23 2014
%F G.f. A(x) satisifies A(x) = 1 + x*A(x)^2*(2 - G(x*A(x)^2))*G(x*A(x)^2)^2, where G(x) = 1 + x*G(x)^4 is the g.f. of A002293. - _Paul D. Hanna_, Aug 25 2014
%t CoefficientList[Series[((1-12*x)^(3/2) + (1+36*x)) / (2*(4*x+1)^2),{x,0,20}],x] (* _Vaclav Kotesovec_, Aug 23 2014 *)
%o (PARI) x='x+O('x^50); Vec(((1-12*x)^(3/2)+(1+36*x))/(2*(4*x+1)^2)) \\ _Altug Alkan_, Nov 25 2015
%Y Cf. A220911.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Jan 02 2013
%E a(11)-a(23) by _Karol A. Penson_ and Wojciech Mlotkowski, Aug 04 2013
%E Prepended a(0)=1 from _Vaclav Kotesovec_, Aug 23 2014
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