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A005492
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From expansion of falling factorials.
(Formerly M3495)
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2
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4, 15, 52, 151, 372, 799, 1540, 2727, 4516, 7087, 10644, 15415, 21652, 29631, 39652, 52039, 67140, 85327, 106996, 132567, 162484, 197215, 237252, 283111, 335332, 394479, 461140, 535927, 619476, 712447, 815524, 929415, 1054852, 1192591, 1343412, 1508119, 1687540
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OFFSET
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4,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=4..40.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
E. G. Whitehead, Jr., Stirling number identities from chromatic polynomials, J. Combin. Theory, A 24 (1978), 314-317.
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) = 5a(n-1) - 10a(n-2) + 10a(n-3) - 5a(n-4) + a(n-5).
a(n) = n^4 - 16n^3 + 102n^2 - 300n + 340.
G.f.: x^4*(-7*x^4-x^3-17*x^2+5*x-4)/(x-1)^5. - Harvey P. Dale, Dec 25 2012
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MAPLE
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A005492:=-(15-23*z+41*z**2-13*z**3+4*z**4)/(z-1)**5; # Conjectured by Simon Plouffe in his 1992 dissertation. Gives sequence except for the leading 4.
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MATHEMATICA
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LinearRecurrence[{5, -10, 10, -5, 1}, {4, 15, 52, 151, 372}, 50] (* Harvey P. Dale, Dec 25 2012 *)
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CROSSREFS
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Row n=4 of A108087 (shifted and first term prepended).
Cf. A005490.
Sequence in context: A303843 A107307 A240365 * A003013 A117202 A291011
Adjacent sequences: A005489 A005490 A005491 * A005493 A005494 A005495
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Simon Plouffe
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EXTENSIONS
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More terms from Pab Ter (pabrlos(AT)yahoo.com), May 09 2004
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STATUS
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approved
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