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%I #12 Oct 18 2023 02:11:04
%S 1,1,2,6,17,54,178,606,2116,7533,27242,99799,369583,1381309,5203599,
%T 19737935,75321337,288968031,1113893815,4312073256,16756934181,
%U 65345024968,255625711296,1002888257745,3945055462020,15556613282788
%N Expansion of g.f.: (1+x-sqrt(1-2*x-7*x^2-8*x^3-4*x^4))/(2*(1+x+x^2)).
%H G. C. Greubel, <a href="/A108630/b108630.txt">Table of n, a(n) for n = 1..1000</a>
%F Conjecture D-finite with recurrence: (n-1)*a(n) = (n-4)*a(n-1) +8*(n-4)*a(n-2) +(17*n-77)*a(n-3) +(19*n-100)*a(n-4) +12*(n-6)*a(n-5) +4*(n-7)*a(n-6). - _R. J. Mathar_, Sep 27 2014
%t Rest@CoefficientList[Series[(1+x-Sqrt[1-2*x-7*x^2-8*x^3-4*x^4])/(2*(1+ x+x^2)), {x,0,35}], x] (* _G. C. Greubel_, Oct 18 2023 *)
%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 36); Coefficients(R!( (1+x-Sqrt(1-2*x-7*x^2-8*x^3-4*x^4))/(2*(1+x+x^2)) )); // _G. C. Greubel_, Oct 18 2023
%o (Sage)
%o def A108630_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (1+x-sqrt(1-2*x-7*x^2-8*x^3-4*x^4))/(2*(1+x+x^2)) ).list()
%o a=A108630_list(36); a[1:] # _G. C. Greubel_, Oct 18 2023
%Y Cf. A039985.
%K nonn
%O 1,3
%A _Christian G. Bower_, Jun 12 2005
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