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%I #14 Jan 30 2020 21:29:17
%S 0,0,0,2,38,322,2112,12210,65494,334334,1647776,7910916,37216060,
%T 172263652,786879680,3554999370,15912092070,70656410550,311584194240,
%U 1365760098780,5954667085620,25839361664220,111651277670400,480603648082740,2061623609421948,8815899506583852,37590408710959552
%N G.f.: (P-Q*(sqrt(1-4*x)))/(x*(1-4*x)^3) where P=(1-4*x)^3*(1-x-x^2), Q=1-11*x+39*x^2-40*x^3-22*x^4.
%H Luca Ferrari and Emanuele Munarini, <a href="http://arxiv.org/abs/1203.6807">Enumeration of saturated chains in Dyck lattices</a>, arXiv preprint arXiv:1203.6807, 2012
%F Conjecture D-finite with recurrence: -(n+1)*(423*n-1718)*a(n) +(-423*n^2+4779*n+1718)*a(n-1) +(17801*n^2-84527*n+75390)*a(n-2) -2*(9341*n-20828)*(2*n-7)*a(n-3)=0. - _R. J. Mathar_, Jan 25 2020
%t gf = (P-Q(Sqrt[1 - 4x]))/(x (1 - 4x)^3) /. P -> (1 - 4x)^3 (1 - x - x^2) /. Q -> 1 - 11x + 39x^2 - 40x^3 - 22x^4;
%t CoefficientList[gf + O[x]^27, x] (* _Jean-François Alcover_, Oct 08 2018 *)
%Y Cf. A217215.
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Oct 03 2012
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