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1, 2, 9, 50, 310, 2056, 14273, 102410, 753390, 5651948, 43074218, 332553252, 2595442616, 20443630100, 162308182577, 1297503030106, 10435055801110, 84371602316812, 685424273207630, 5592040955107420, 45798007929729828
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{k = 1..n} A211788(n,k).
G.f. A(x) satisfies: A(x) = x*((1-A(x))/(1-2*A(x)))^2, a(n) = (Sum_{i=0..n-1} 2^i*(-1)^(n-i-1)*binomial(2*n,n-i-1)*binomial(2*n+i-1,2*n-1))/n for n > 0, a(0)=0. [Vladimir Kruchinin, Feb 08 2013]
Recurrence: 4*n*(2*n - 1)*(17*n - 27)*a(n) = (1207*n^3 - 4331*n^2 + 4818*n - 1584)*a(n-1) - 2*(n-3)*(2*n - 3)*(17*n - 10)*a(n-2).
a(n) ~ sqrt(21/sqrt(17)-5) * ((71 + 17*sqrt(17))/16)^n / (sqrt(8*Pi) * n^(3/2)). (End)
a(n+1) = (1/(n+1)) * Sum_{k=0..n} binomial(2*n+k+1,k) * binomial(n-1,n-k). - Seiichi Manyama, Jan 12 2024
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MATHEMATICA
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Rest[CoefficientList[InverseSeries[Series[x*(2*x-1)^2/(x-1)^2, {x, 0, 30}], x], x]] (* Vaclav Kotesovec, Nov 05 2017 *)
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PROG
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(PARI) N=21; x='x+O('x^(N+1)); Vec(serreverse(x*((1-2*x)/(1-x))^2)) \\ Gheorghe Coserea, Nov 05 2017
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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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