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A141353
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a(n) = Catalan(n) + 2^n - 0^n.
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2
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1, 3, 6, 13, 30, 74, 196, 557, 1686, 5374, 17820, 60834, 212108, 751092, 2690824, 9727613, 35423206, 129775862, 477900844, 1767787478, 6565168996, 24468364172, 91486757944, 343068002258, 1289920924540, 4861979955884
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: c(x)+2x/(1-2x), where c(x) is the g.f. of A000108. [corrected by Paul Barry, Oct 18 2010]
Conjecture: (n+1)*a(n) + 2*(-4*n+1)*a(n-1) + 4*(5*n-7)*a(n-2) + 8*(-2*n+5)*a(n-3) = 0. - R. J. Mathar, Nov 15 2012
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MATHEMATICA
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f[n_] := Binomial[2n, n]/(n + 1) + 2^n - 0^n; f[0] = 1; Array[f, 29, 0] (* or *)
CoefficientList[ Series[1 + 1/2 (-4 + 2/(1 - 2x) + (1 - Sqrt[1 - 4x])/x), {x, 0, 28}], x] (* Robert G. Wilson v, Mar 18 2018 *)
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PROG
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(PARI) a(n) = binomial(2*n, n)/(n+1) + 2^n - 0^n; \\ Michel Marcus, Mar 18 2018
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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