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%I #13 Jan 30 2020 21:29:16
%S 0,0,0,0,0,0,-16,0,80,240,656,1936,6000,19088,61792,202832,673888,
%T 2263392,7677712,26280800,90709616,315486768,1104982560,3895248720,
%U 13813470240,49256281920,176536299168,635710344672,2299280127328,8350257302304,30441306959040
%N G.f.: (x^2+x-1)*(1+2*x+S)*(1-5*x+2*x^2+(3*x-1)*S)^2*(-1+3*x+2*x^2+(1-x)*S), where S=sqrt(1-4*x).
%D C. K. Fan, Structure of a Hecke algebra quotient, J. Amer. Math. Soc., 10 (1997), 139-167. [See D(y) on p. 158.]
%H Vincenzo Librandi, <a href="/A135925/b135925.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ 11*2^(2*n-13)/(sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Jun 29 2013
%F Conjecture D-finite with recurrence: +4*(n-1)*(7678757997599*n-100709801435251)*a(n) +(-291262905844111*n^2+4745710679447853*n-12935393149282124)*a(n-1) +3*(268523622217993*n^2-4978734571371597*n+20251709258114720)*a(n-2) +2*(-196528865827703*n^2+4147266222561252*n-21888137659762186)*a(n-3) -12*(22463548140013*n-247087251730058)*(2*n-25)*a(n-4)=0. - _R. J. Mathar_, Jan 23 2020
%p S:=sqrt(1-4*y); Dy:=(y^2+y-1)*(1+2*y+S)*(1-5*y+2*y^2+(3*y-1)*S)^2*(-1+3*y+2*y^2+(1-y)*S);
%t CoefficientList[Series[(x^2 + x - 1) (1 + 2 x + Sqrt[1 - 4 x]) (1 - 5 x + 2 x^2 + (3 x - 1) Sqrt[1 - 4 x])^2 (-1 + 3 x + 2 x^2 + (1 - x) Sqrt[1 - 4 x]), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 30 2016 *)
%Y Cf. A135926.
%K sign
%O 0,7
%A _N. J. A. Sloane_, Mar 09 2008
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