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A132374
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Expansion of c(7*x^2)/(1 - x*c(7*x^2)), where c(x) is the g.f. of A000108.
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10
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1, 1, 8, 15, 120, 274, 2192, 5531, 44248, 118686, 949488, 2654646, 21237168, 61189668, 489517344, 1443039123, 11544312984, 34648845862, 277190766896, 844131474530, 6753051796240, 20813234394492, 166505875155936, 518373091849502
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OFFSET
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0,3
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COMMENTS
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Hankel transform is 7^C(n+1,2).
Series reversion of x*(1+x)*(1+2*x+8*x^2).
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} A120730(n,k) * 7^(n-k).
a(n) = 4*( 2*(n+1)*a(n-1) + 7*(n-2)*a(n-2) - 56*(n-2)*a(n-3) )/(n+1).
G.f.: (1 - sqrt(1 - 28*x^2))/(14*x^2 - x*(1 - sqrt(1 - 28*x^2))). (End)
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MATHEMATICA
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CoefficientList[Series[(1-Sqrt[1-28*x^2])/(14*x^2 -x*(1-Sqrt[1-28*x^2])), {x, 0, 40}], x] (* G. C. Greubel, Nov 08 2022 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( (1-Sqrt(1-28*x^2))/(14*x^2 -x*(1-Sqrt(1-28*x^2))) )); // G. C. Greubel, Nov 08 2022
(SageMath)
def A120730(n, k): return 0 if (n>2*k) else binomial(n, k)*(2*k-n+1)/(k+1)
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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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