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 A005492 From expansion of falling factorials. (Formerly M3495) 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS 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). FORMULA 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 MAPLE 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. MATHEMATICA LinearRecurrence[{5, -10, 10, -5, 1}, {4, 15, 52, 151, 372}, 50] (* Harvey P. Dale, Dec 25 2012 *) CROSSREFS 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 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Pab Ter (pabrlos(AT)yahoo.com), May 09 2004 STATUS approved

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Last modified July 3 03:28 EDT 2022. Contains 355030 sequences. (Running on oeis4.)