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A052713
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Expansion of e.g.f. (1-sqrt(1-8*x))/2.
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9
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0, 2, 8, 96, 1920, 53760, 1935360, 85155840, 4428103680, 265686220800, 18066663014400, 1373066389094400, 115337576683929600, 10611057054921523200, 1061105705492152320000, 114599416193152450560000
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OFFSET
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0,2
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COMMENTS
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Has a square root singularity.
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LINKS
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FORMULA
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D-finite with recurrence: a(1)=2, a(n+1) = 4*(2*n -1)*a(n).
a(n+1) = 1/4*8^(n+1)*Gamma(n+1/2)/Pi^(1/2)
G.f.: (1- 2F0([1,-1/2], [], 8*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(S, S), S=Union(Z, C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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Table[n!*2^n*CatalanNumber[n-1] + Boole[n==0], {n, 0, 30}] (* G. C. Greubel, May 29 2022 *)
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PROG
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(SageMath) [2^n*factorial(n)*catalan_number(n-1) + bool(n==0)/2 for n in (0..30)] # G. C. Greubel, May 29 2022
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CROSSREFS
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Cf. A052711, A052712, 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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