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A026773
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a(n) = T(2n-1,n-1), T given by A026769. Also T(2n+1,n+1), T given by A026780.
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11
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1, 4, 17, 76, 352, 1674, 8129, 40156, 201236, 1020922, 5234660, 27089726, 141335846, 742712598, 3927908193, 20891799036, 111688381228, 599841215226, 3234957053984, 17512055200470, 95125188934942, 518340392855286, 2832580291316092, 15520177744727766
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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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G.f.: (sqrt(1-4*x) - sqrt(1-6*x+x^2))/(2*x) -1/2. (End)
a(n) = Sum_{k=0..n} C(n+k+1, n+1)*C(n+1, k)/(k+1).
a(n) = Sum_{k=0..n+1} C(n+2, k)*C(n+k, n+1)}/(n+2). (End)
D-finite with recurrence n*(n+1)*a(n) -n*(11*n-7)*a(n-1) +(37*n^2-95*n+54)*a(n-2) +(-49*n^2+269*n-354)*a(n-3) +6*(9*n^2-71*n+138)*a(n-4) -4*(2*n-9)*(n-5)*a(n-5)=0. - R. J. Mathar, Aug 05 2021
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MAPLE
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seq(coeff(series((sqrt(1-4*x) - sqrt(1-6*x+x^2))/(2*x) -1/2, x, n+1), x, n), n = 0..30); # G. C. Greubel, Nov 01 2019
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MATHEMATICA
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Rest@CoefficientList[Series[(Sqrt[1-4*x] - Sqrt[1-6*x+x^2])/(2*x) -1/2, {x, 0, 30}], x] (* G. C. Greubel, Nov 01 2019 *)
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PROG
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(PARI) my(x='x+O('x^30)); Vec((sqrt(1-4*x) - sqrt(1-6*x+x^2))/(2*x) -1/2) \\ G. C. Greubel, Nov 01 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (Sqrt(1-4*x) - Sqrt(1-6*x+x^2))/(2*x) -1/2 )); // G. C. Greubel, Nov 01 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P((sqrt(1-4*x) - sqrt(1-6*x+x^2))/(2*x) -1/2).list()
(GAP) List([0..30], n-> Sum([0..n], k-> Binomial(n+1, k)*Binomial(n+k+1, n+1)/(k+1) )); # G. C. Greubel, Nov 01 2019
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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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