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%I #33 Jan 12 2024 08:44:59
%S 1,2,9,50,310,2056,14273,102410,753390,5651948,43074218,332553252,
%T 2595442616,20443630100,162308182577,1297503030106,10435055801110,
%U 84371602316812,685424273207630,5592040955107420,45798007929729828
%N Row sums of A211788.
%H Gheorghe Coserea, <a href="/A211789/b211789.txt">Table of n, a(n) for n = 1..303</a>
%F a(n) = Sum_{k = 1..n} A211788(n,k).
%F 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]
%F From _Vaclav Kotesovec_, Nov 05 2017: (Start)
%F 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).
%F a(n) ~ sqrt(21/sqrt(17)-5) * ((71 + 17*sqrt(17))/16)^n / (sqrt(8*Pi) * n^(3/2)). (End)
%F 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
%t Rest[CoefficientList[InverseSeries[Series[x*(2*x-1)^2/(x-1)^2, {x, 0, 30}], x], x]] (* _Vaclav Kotesovec_, Nov 05 2017 *)
%o (PARI) N=21; x='x+O('x^(N+1)); Vec(serreverse(x*((1-2*x)/(1-x))^2)) \\ _Gheorghe Coserea_, Nov 05 2017
%Y Cf. A211788.
%K nonn,easy
%O 1,2
%A _Peter Bala_, Aug 02 2012
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