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%I #13 Apr 06 2017 02:24:05
%S 0,0,1,12,98,684,4403,27048,161412,945288,5466549,31340628,178604998,
%T 1013573652,5735117479,32385232272,182622362504,1028897389008,
%U 5793703249449,32615362319580,183593293074730,1033535639454780,5819389057957211,32775522041862072,184658694508103180
%N Second convolution of A065096.
%H Fung Lam, <a href="/A238755/b238755.txt">Table of n, a(n) for n = 0..1300</a>
%F G.f. = (G.f. of A065096)^2.
%F Recurrence: (n+6)*a(n) = 225*(6-n)*a(n-8) + 1020*(2*n-9)*a(n-7) + 5164*(3-n)*a(n-6) + 76*(78*n-117)*a(n-5) - 3590*n*a(n-4) + 36*(34*n+51)*a(n-3) - 236*(n+3)*a(n-2) + 12*(2*n+9)*a(n-1), n>=8.
%F Recurrence (of order 2): (n-2)*(n+6)*a(n) = 3*(n+1)*(2*n+3)*a(n-1) - n*(n+1)*a(n-2). - _Vaclav Kotesovec_, Mar 05 2014
%F a(n) ~ (3*sqrt(2)-4)^(7/2) * (3+2*sqrt(2))^(n+6) / (8*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Mar 05 2014
%t CoefficientList[Series[(1-3*x-Sqrt[1-6*x+x^2])^4/(16*x^3)^2, {x, 0, 20}], x] (* _Vaclav Kotesovec_, Mar 05 2014 *)
%o (PARI) x='x+O('x^50); concat([0,0], Vec((1-3*x-sqrt(1-6*x+x^2))^4/(16*x^3)^2)) \\ _G. C. Greubel_, Apr 05 2017
%Y Cf. A065096, A000108, A001003.
%K nonn,easy
%O 0,4
%A _Fung Lam_, Mar 04 2014