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A162480
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Expansion of 1/((1-x)^2*sqrt(1-4x/(1-x)^4)).
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1
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1, 4, 21, 126, 797, 5190, 34439, 231556, 1572135, 10754148, 74001735, 511686726, 3552251429, 24743806370, 172853699427, 1210514603212, 8495774193707, 59739915525288, 420785972800187, 2968344133842182, 20967995689677183
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: 1/((1-x)^2-2x/((1-x)^2-x/((1-x)^2-x/((1-x)^2-... (continued fraction);
a(n) = Sum_{k=0..n} C(n+3k+1,n-k)*A000984(k).
D-finite with recurrence: n*a(n) +4*(1-2n)*a(n-1) +6*(n-1)*a(n-2) +2*(3-2n)*a(n-3) +(n-2)*a(n-4)=0. - R. J. Mathar, Nov 17 2011
G.f.: 1/sqrt(1-8*t+6*t^2-4*t^3+t^4). Remark: using this form of the g.f., it is easy to prove the above recurrence. - Emanuele Munarini, Aug 31 2017
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MATHEMATICA
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CoefficientList[Series[1/((1-x)^2 Sqrt[1-4 x/(1-x)^4]), {x, 0, 20}], x] (* Harvey P. Dale, Jun 28 2017 *)
Table[Sum[Binomial[n+3k+1, 4k+1]Binomial[2k, k], {k, 0, n}], {n, 0, 100}] (* Emanuele Munarini, Aug 31 2017 *)
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PROG
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(Maxima) makelist(sum(binomial(n+3*k+1, 4*k+1)*binomial(2*k, k), k, 0, n), n, 0, 12); /* Emanuele Munarini, Aug 31 2017 */
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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