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A037237
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Expansion of (3 + x^2) / (1 - x)^4.
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5
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3, 12, 31, 64, 115, 188, 287, 416, 579, 780, 1023, 1312, 1651, 2044, 2495, 3008, 3587, 4236, 4959, 5760, 6643, 7612, 8671, 9824, 11075, 12428, 13887, 15456, 17139, 18940, 20863, 22912, 25091, 27404
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (2*(k+1)^2 + 1). - Mike Warburton, Jul 07 2007, Sep 07 2007
a(n) = (n+1)*(2*n^2 + 7*n + 9)/3. - R. J. Mathar, Mar 29 2010
E.g.f.: (1/3)*(9 + 27*x + 15*x^2 + 2*x^3)*exp(x). - G. C. Greubel, Jul 22 2017
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MATHEMATICA
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CoefficientList[Series[(3+x^2)/(1-x)^4, {x, 0, 50}], x] (* Harvey P. Dale, Mar 06 2011 *)
LinearRecurrence[{4, -6, 4, -1}, {3, 12, 31, 64}, 40] (* Vincenzo Librandi Jun 21 2012 *)
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PROG
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(Magma) I:=[3, 12, 31, 64]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)- Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 21 2012
(PARI) x='x+O('x^50); Vec((3+x^2)/(1-x)^4) \\ G. C. Greubel, Jul 22 2017
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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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