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A081584
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Fourth row of Pascal-(1,2,1) array A081577.
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3
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1, 13, 79, 307, 886, 2086, 4258, 7834, 13327, 21331, 32521, 47653, 67564, 93172, 125476, 165556, 214573, 273769, 344467, 428071, 526066, 640018, 771574, 922462, 1094491, 1289551, 1509613, 1756729, 2033032, 2340736, 2682136, 3059608
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OFFSET
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0,2
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COMMENTS
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Equals binomial transform of [1, 12, 54, 108, 81, 0, 0, 0, ...] where (1, 12, 54, 108, 81) = row 4 of triangle A013610. - Gary W. Adamson, Jul 19 2008
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LINKS
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FORMULA
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a(n) = (8 + 6*n + 81*n^2 - 18*n^3 + 27*n^4)/8.
G.f.: (1+2*x)^4/(1-x)^5.
E.g.f.: (1/8)*(8 + 96*x + 216*x^2 + 144*x^3 + 27*x^4)*exp(x). - G. C. Greubel, May 26 2021
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MAPLE
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seq((8+6*n+81*n^2-18*n^3+27*n^4)/8, n=0..40); # G. C. Greubel, May 26 2021
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MATHEMATICA
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CoefficientList[Series[(1+2x)^4/(1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 09 2013 *)
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PROG
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(Magma) [(8+6*n+81*n^2-18*n^3+27*n^4)/8: n in [0..40]]; // Vincenzo Librandi, Aug 09 2013
(Sage) [(8+6*n+81*n^2-18*n^3+27*n^4)/8 for n in (0..40)] # G. C. Greubel, May 26 2021
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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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