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A052711
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Expansion of e.g.f. x*(1 - 2*x - sqrt(1-4*x))/2.
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9
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0, 0, 0, 6, 48, 600, 10080, 211680, 5322240, 155675520, 5189184000, 194075481600, 8045310873600, 366061644748800, 18134130709094400, 971471287987200000, 55956746188062720000, 3448334483839365120000
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OFFSET
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0,4
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LINKS
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FORMULA
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D-finite with recurrence: a(1)=0, a(2)=0, a(3)=6, a(4)=48, n*a(n+1) = 2*(n+1)*(2*n-3)*a(n).
G.f.: x*(1 - 4*x - 2F0([-1/2,2], [], 4*x))/2. - R. J. Mathar, Jan 25 2020
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MAPLE
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spec := [S, {C=Union(B, Z), B=Prod(C, C), S=Prod(B, Z)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[x (1-2x-Sqrt[1-4x])/2, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 05 2016 *)
Table[n!*CatalanNumber[n-2] +Boole[n==1] -2*Boole[n==2], {n, 0, 30}] (* G. C. Greubel, May 30 2022 *)
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PROG
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(SageMath) [factorial(n)*catalan_number(n-2) + bool(n==1)/2 - 2*bool(n==2) for n in (0..30)] # G. C. Greubel, May 30 2022
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CROSSREFS
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Cf. A052712, A052713, A052714, A052715, A052716, A052717, A052718, A052719, A052720, A052721, A052722, A052723.
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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STATUS
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approved
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