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A052721
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Expansion of e.g.f. x*(1-2*x)*(1 - 2*x - sqrt(1-4*x))/2 - x^3.
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9
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0, 0, 0, 0, 0, 120, 2880, 70560, 1935360, 59875200, 2075673600, 79913433600, 3387499315200, 156883562035200, 7884404656128000, 427447366714368000, 24869664972472320000, 1545805113445232640000, 102232975285590589440000
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OFFSET
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0,6
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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(4)=0, a(3)=0, a(5)=120, a(6)=2880, (n+2)*a(n+2) = (6*n^2 + 8*n - 8)*a(n+1) + (40 + 44*n = 4*n^2 - 8*n^3)*a(n).
a(n) = 2*Pi^(-1/2)*4^(n-3)*Gamma(n-5/2)*n*(n-4) for n>3. - Mark van Hoeij, Oct 30 2011
G.f.: 4!*x*(d/dx)( x^5 * Hypergeometric2F0([2, 5/2], [], 4*x) ).
E.g.f.: (x/2)*(1 - 4*x + 2*x^2 - (1-2*x)*sqrt(1-4*x)). (End)
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MAPLE
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spec := [S, {C=Union(B, Z), B=Prod(C, C), S=Prod(B, B, Z)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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Table[If[n<5, 0, 2*n*(n-2)!*(n-4)*CatalanNumber[n-3]], {n, 0, 30}] (* G. C. Greubel, May 28 2022 *)
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PROG
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(SageMath)
if (n<5): return 0
else: return 2*n*factorial(n-2)*(n-4)*catalan_number(n-3)
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CROSSREFS
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Cf. A052711, A052712, A052713, A052714, A052715, A052716, A052717, A052718, A052719, A052720, 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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