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A161701
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a(n) = (n^5 - 5*n^4 + 5*n^3 + 5*n^2 + 114*n + 120)/120.
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20
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1, 2, 3, 4, 6, 12, 28, 64, 135, 262, 473, 804, 1300, 2016, 3018, 4384, 6205, 8586, 11647, 15524, 20370, 26356, 33672, 42528, 53155, 65806, 80757, 98308, 118784, 142536, 169942, 201408, 237369, 278290, 324667, 377028, 435934, 501980, 575796, 658048
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OFFSET
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0,2
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COMMENTS
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{a(k): 0 <= k < 6} = divisors of 12:
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LINKS
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FORMULA
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a(n) = C(n,0) + C(n,1) + C(n,4) + C(n,5).
G.f.: (1-4*x+6*x^2-4*x^3+2*x^4)/(1-x)^6. - Colin Barker, Aug 20 2012
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EXAMPLE
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Differences of divisors of 12 to compute the coefficients of their interpolating polynomial, see formula:
1 2 3 4 6 12
1 1 1 2 6
0 0 1 4
0 1 3
1 2
1
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MAPLE
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MATHEMATICA
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CoefficientList[Series[(1-4*x+6*x^2-4*x^3+2*x^4)/(1-x)^6, {x, 0, 50}], x] (* G. C. Greubel, Jul 16 2017 *)
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PROG
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(Magma) [(n^5 - 5*n^4 + 5*n^3 + 5*n^2 + 114*n + 120)/120: n in [0..50]]; // Vincenzo Librandi, Dec 27 2010
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CROSSREFS
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Cf. A000124, A000125, A000127, A002522, A005408, A006261, A016813, A058331, A080856, A086514, A161702, A161703, A161704, A161706, A161707, A161708, A161710, A161711, A161712, A161713, A161715.
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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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