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 A006348 a(n) = (n+2)*a(n-1) + (-1)^n. (Formerly M3609) 1
 0, 1, 4, 25, 174, 1393, 12536, 125361, 1378970, 16547641, 215119332, 3011670649, 45175059734, 722800955745, 12287616247664, 221177092457953, 4202364756701106, 84047295134022121, 1764993197814464540, 38829850351918219881, 893086558094119057262 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) is a function of the subfactorials... a(n) = A000166(n+2) - 1/3*(n+2)! /Q, i.e., ... 1 = 9 - 24/3, 4 = 44 - 120/3, 25 = 265 - 720/3 ... - Gary Detlefs, Dec 17 2009 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Robert Israel, Table of n, a(n) for n = 1..448 J. A. Sharp & N. J. A. Sloane, Correspondence, 1977 FORMULA a(n) = (n+1)(a(n-1) + a(n-2)). - Gary Detlefs, Dec 17 2009 E.g.f. with offset 0: ((2 + 3*x + x^3)*exp(-x) - 2)/(1 - x)^4. From int(((9 + 8*x + 6*x^2 + x^4)*exp(-x) - 8)/(1 - x)^5, x) with input 0 for x = 0. - Wolfdieter Lang, May 03 2010 From Robert Israel, Feb 28 2017: (Start) a(n) = Gamma(n+3, -1)/e - (n+2)!/3. a(n) ~ (1/e - 1/3) sqrt(2 Pi) n^(n+5/2) exp(-n). (End) MAPLE a:= n-> (n+2)!*sum((-1)^k/k!, k=4..n+2): seq(a(n), n=1..23); # Zerinvary Lajos, May 25 2007 a:= n-> floor(((n+2)!+1)/exp(1)) -(n+2)!/3: seq(a(n), n=1..23); # Gary Detlefs, Dec 17 2009 CROSSREFS Sequence in context: A034494 A084210 A093683 * A213608 A324169 A213231 Adjacent sequences:  A006345 A006346 A006347 * A006349 A006350 A006351 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified May 15 10:34 EDT 2021. Contains 343909 sequences. (Running on oeis4.)