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A081893
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Third binomial transform of C(n+2,2).
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3
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1, 6, 33, 172, 864, 4224, 20224, 95232, 442368, 2031616, 9240576, 41680896, 186646528, 830472192, 3674210304, 16173236224, 70866960384, 309237645312, 1344324763648, 5823975653376, 25151328485376, 108301895335936
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OFFSET
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0,2
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COMMENTS
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3rd binomial transform of C(n+2,2), A000217.
4th binomial transform of (1,2,1,0,0,0,.....)
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LINKS
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FORMULA
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a(n) = 4^n*(n^2 + 15*n + 32)/32.
G.f.: (1 - 3*x)^2/(1 - 4*x)^3.
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MATHEMATICA
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LinearRecurrence[{12, -48, 64}, {1, 6, 33}, 50] (* G. C. Greubel, Oct 18 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec((1-3*x)^2/(1-4*x)^3) \\ G. C. Greubel, Oct 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-3*x)^2/(1-4*x)^3)); // G. C. Greubel, Oct 18 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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