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A081916
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a(n) = 5^n*(n^3 - 3n^2 + 2n + 750)/750.
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3
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1, 5, 25, 126, 645, 3375, 18125, 100000, 565625, 3265625, 19140625, 113281250, 673828125, 4013671875, 23876953125, 141601562500, 836181640625, 4913330078125, 28717041015625, 166931152343750, 965118408203125
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A081915. 5th binomial transform of (1,0,0,1,0,0,0,0,...). Case k=5 where a(n,k) = k^n*(n^3 - 3n^2 + 2n + 6k^3)/(6k^3), with g.f. (1 - 3kx + 3k^2x^2 - (k^3-1)x^3)/(1-kx)^4.
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LINKS
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FORMULA
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a(n) = 5^n*(n^3 - 3n^2 + 2n + 750)/750.
G.f.: (1 - 15x + 75x^2 - 124x^3)/(1-5x)^4.
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MATHEMATICA
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a[n_]:= 5^n*(n^3 - 3n^2 + 2n + 750)/750 ; Array[a, 40, 0] (* or *)
CoefficientList[Series[(1 - 15x + 75x^2 - 124x^3)/(1-5x)^4 , {x, 0, 40}], x] (* Stefano Spezia, Sep 02 2018 *)
LinearRecurrence[{20, -150, 500, -625}, {1, 5, 25, 126}, 30] (* Harvey P. Dale, Jun 29 2021 *)
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PROG
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(Magma) [5^n*(n^3-3*n^2+2*n+750)/750: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011
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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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