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%I #13 Apr 04 2020 10:30:51
%S 0,0,0,0,0,2,4,6,15,31,67,155,343,787,1829,4233,9940,23454,55540,
%T 132390,316704,760462,1833050,4431552,10745282,26125316,63672044,
%U 155536070,380739734,933832952,2294581836,5647750518,13923153431,34375447863,84989987987,210407135915,521547749731,1294310608775,3215632551785,7997467696213,19910095233857
%N From the enumeration of involutions avoiding the pattern 4321.
%H Piera Manara and Claudio Perelli Cippo, <a href="http://www.mat.unisi.it/newsito/puma/public_html/22_2/manara_perelli-cippo.pdf">The fine structure of 4321 avoiding involutions and 321 avoiding involutions</a>, PU. M. A. Vol. 22 (2011), 227-238; See Theorem 4.2.
%F Manara and Cippo give a g.f.
%p A217525 := proc(nmax)
%p local x ;
%p -4+4/(1+x^2)+1/(1+x)^2 ;
%p 1/(1+x)-2*x^2*(1+x)-sqrt(%) ;
%p taylor(%/2,x=0,nmax+1) ;
%p seq(coeftayl(%,x=0,n),n=0..nmax) ;
%p end proc: # _R. J. Mathar_, Nov 05 2012
%t a[n_] := SeriesCoefficient[(1/2)(-2(x+1)x^2 - Sqrt[4/(x^2+1) + 1/(x+1)^2 - 4] + 1/(x+1)), {x, 0, n}];
%t a /@ Range[0, 40] (* _Jean-François Alcover_, Apr 04 2020 *)
%K nonn
%O 0,6
%A _N. J. A. Sloane_, Oct 13 2012
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