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A099324
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Expansion of (1 + sqrt(1 + 4x))/(2(1 + x)).
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3
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1, 0, -1, 3, -8, 22, -64, 196, -625, 2055, -6917, 23713, -82499, 290511, -1033411, 3707851, -13402696, 48760366, -178405156, 656043856, -2423307046, 8987427466, -33453694486, 124936258126, -467995871776, 1757900019100, -6619846420552, 24987199492704, -94520750408708
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{k=0..2n} (2*0^(2n-k)-1)*C(k,floor(k/2)). - Paul Barry, Aug 10 2009
G.f.: T(0)/(2+2*x)), where T(k) = k+2 - 2*x*(2*k+1) + 2*x*(k+2)*(2*k+3)/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 27 2013
D-finite with recurrence: (2+4*n)*a(n) + (4+5*n)*a(n+1) + (n+2)*a(n+2) = 0. - Robert Israel, Mar 27 2018
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MAPLE
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f:= gfun:-rectoproc({(2+4*n)*a(n)+(4+5*n)*a(n+1)+(n+2)*a(n+2), a(0) = 1, a(1) = 0}, a(n), remember):
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MATHEMATICA
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CoefficientList[Series[(1+Sqrt[1+4x])/(2(1+x)), {x, 0, 40}], x] (* Harvey P. Dale, Jan 30 2014 *)
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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