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A024002
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a(n) = 1 - n^4.
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5
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1, 0, -15, -80, -255, -624, -1295, -2400, -4095, -6560, -9999, -14640, -20735, -28560, -38415, -50624, -65535, -83520, -104975, -130320, -159999, -194480, -234255, -279840, -331775, -390624, -456975, -531440, -614655, -707280, -809999, -923520, -1048575, -1185920, -1336335, -1500624
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..630
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
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a(n) = -A123865(n) for n>0.
From G. C. Greubel, May 11 2017: (Start)
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: (1 - 5*x - 5*x^2 - 15*x^3)/(1 - x)^5.
E.g.f.: (1 - x - 7*x^2 - 6*x^3 - x^4)*exp(x). (End)
Sum_{k>=2} -1/a(k) = A256919 = 7/8 - Pi*coth(Pi)/4. - Vaclav Kotesovec, Dec 08 2020
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MATHEMATICA
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Table[1 - n^4, {n, 0, 50}] (* Bruno Berselli, Jun 12 2015 *)
CoefficientList[Series[(1 - 5*x - 5*x^2 - 15*x^3)/(1 - x)^5, {x, 0, 50}], x] (* G. C. Greubel, May 11 2017 *)
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PROG
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(MAGMA) [1-n^4: n in [0..50]]; // Vincenzo Librandi, Apr 29 2011
(PARI) x='x+O('x^50); Vec((1 - 5*x - 5*x^2 - 15*x^3)/(1 - x)^5) \\ G. C. Greubel, May 11 2017
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CROSSREFS
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Cf. A123865, .
Sequence in context: A033594 A059377 A123865 * A050149 A055815 A338414
Adjacent sequences: A023999 A024000 A024001 * A024003 A024004 A024005
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KEYWORD
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sign,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Corrected by T. D. Noe, Nov 08 2006
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STATUS
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approved
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