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A269796
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a(n) = 4^n * A000108(n+1).
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1
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1, 8, 80, 896, 10752, 135168, 1757184, 23429120, 318636032, 4402970624, 61641588736, 872465563648, 12463793766400, 179478630236160, 2602440138424320, 37965009078190080, 556820133146787840, 8205770383215820800, 121445401671594147840, 1804331681977970196480, 26900945076762464747520
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1 - sqrt(1 - 16*x) - 8*x)/(32*x^2). - Bruno Berselli, Mar 07 2016
Sum_{n>=0} 1/a(n) = 52/75 + 512*arcsin(1/4)/(75*sqrt(15)).
Sum_{n>=0} (-1)^n/a(n) = 164/289 + 1536*arcsinh(1/4)/(289*sqrt(17)). (End)
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MATHEMATICA
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Table[4^n CatalanNumber[n + 1], {n, 0, 20}] (* Bruno Berselli, Mar 07 2016 *)
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PROG
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(PARI) cat(n) = binomial(2*n, n)/(n+1);
a(n) = 4^n*cat(n+1);
(Sage) [4^n*catalan_number(n+1) for n in (0..20)] # Bruno Berselli, Mar 07 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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