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A132864
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Expansion of 1/(1-4x*c(5x)), where c(x) is the g.f. of A000108.
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3
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1, 4, 36, 424, 5716, 83544, 1288296, 20637264, 340116276, 5730014584, 98241641656, 1708602483504, 30070563388936, 534554579527024, 9584333758817616, 173120386421418144, 3147337611202622196, 57545643875054919864, 1057492201661230657176
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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Integral representation: a(n) = (2/Pi)*Integral_{x=0..20} x^n*sqrt(x*(20-x))/(x*(16+x)). - Paul Barry, Sep 15 2009
a(n) = upper left term in M^n, M = an infinite square production matrix as follows:
4, 4, 0, 0, 0, 0, ...
5, 5, 5, 0, 0, 0, ...
5, 5, 5, 5, 0, 0, ...
5, 5, 5, 5, 5, 0, ...
5, 5, 5, 5, 5, 5, ...
... (End)
Conjecture: n*a(n) + 2*(15-2*n)*a(n-1) + 160*(3-2*n)*a(n-2) = 0. - R. J. Mathar, Nov 15 2011
a(n) ~ 4^n * 5^(n+1) / (9 * n^(3/2) * sqrt(Pi)). - Vaclav Kotesovec, Feb 08 2014
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MATHEMATICA
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CoefficientList[Series[1/(1-4*x*(1-Sqrt[1-20*x])/(10*x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 08 2014 *)
Table[5^(n + 1) * CatalanNumber[n] * Hypergeometric2F1[1, n + 1/2, n + 2, -5/4]/4, {n, 0, 18}] (* Vaclav Kotesovec, Jun 05 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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