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A272871
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Imaginary part of (n + i)^4.
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2
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0, 0, 24, 96, 240, 480, 840, 1344, 2016, 2880, 3960, 5280, 6864, 8736, 10920, 13440, 16320, 19584, 23256, 27360, 31920, 36960, 42504, 48576, 55200, 62400, 70200, 78624, 87696, 97440, 107880, 119040, 130944, 143616, 157080, 171360, 186480, 202464, 219336
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = 4*(n-1)*n*(n+1).
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>3.
G.f.: 24*x^2 / (1-x)^4.
E.g.f.: 4*x^2*(3 + x)*exp(x).
a(n) = 24*binomial(n+1,3).
a(n) = Sum_{k=0..n} A064200(k). (End)
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EXAMPLE
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a(5) = 480 because (5 + i)^4 = 476 + 480*i.
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MATHEMATICA
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Table[Im[(n + I)^4], {n, 0, 38}] (* or *)
Table[4 (n - 1) n (n + 1), {n, 0, 38}] (* or *)
CoefficientList[Series[24 x^2/(1 - x)^4, {x, 0, 38}], x] (* Michael De Vlieger, May 08 2016 *)
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PROG
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(PARI) a(n) = 4*(n-1)*n*(n+1)
(PARI) vector(50, n, n--; imag((n+I)^4))
(PARI) concat(vector(2), Vec(24*x^2/(1-x)^4 + O(x^50)))
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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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