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A052719
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Expansion of e.g.f. (1 - 2*x*sqrt(1-4*x))*(1 - sqrt(1-4*x))/4.
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9
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0, 0, 0, 6, 72, 1080, 20160, 453600, 11975040, 363242880, 12454041600, 476367091200, 20113277184000, 929233405900800, 46630621823385600, 2525825348766720000, 146886458743664640000, 9127944221927731200000
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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(n+2) = (2 + 5*n)*a(n+1) + (6 + 2*n - 4*n^2)*a(n)
G.f.: 6*x^3*Hypergeometric2F0([2, 3/2], [], 4*x).
E.g.f.: (1/4)*(1 + 2*x - 8*x^2 - (1 + 2*x)*sqrt(1-4*x)). (End)
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MAPLE
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spec := [S, {B=Union(Z, C), C=Prod(B, B), S=Prod(B, C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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Table[If[n<2, 0, 3*(n-2)*(n-1)!*CatalanNumber[n-2]], {n, 0, 30}] (* G. C. Greubel, May 28 2022 *)
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PROG
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(SageMath) [0, 0]+[3*(n-2)*factorial(n-1)*catalan_number(n-2) for n in (2..30)] # G. C. Greubel, May 28 2022
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CROSSREFS
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Cf. A052711, A052712, A052713, A052714, A052715, A052716, A052717, A052718, 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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