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A156016
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Expansion of (1-x-sqrt(1-6x-3x^2))/(2x).
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5
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1, 3, 9, 36, 162, 783, 3969, 20817, 112023, 615033, 3431403, 19398690, 110880900, 639730305, 3720657807, 21790419444, 128398625658, 760668489729, 4528069760691, 27070491820644, 162464919528222, 978463778897637
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OFFSET
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0,2
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COMMENTS
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Transform of Catalan numbers by Riordan array ((1+x)/(1-x), x(1+x)/(1-x)^2).
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} Sum_{j=0..k+1} C(k+1,j)*C(n+k-j,n-k-j)*A000108(k).
D-finite with recurrence: (n+1)*a(n) + 3*(-2*n+1)*a(n-1) + 3*(-n+2)*a(n-2) = 0. - R. J. Mathar, Dec 03 2014
G.f. A(x) satisfies: A(x) = 1 + x * (1 + A(x) + A(x)^2). - Ilya Gutkovskiy, Jul 01 2020
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MATHEMATICA
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CoefficientList[Series[(1-x-Sqrt[1-6x-3x^2])/(2x), {x, 0, 30}], x] (* Harvey P. Dale, Jul 27 2014 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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