A006348 a(n) = (n+2)*a(n-1) + (-1)^n. (Formerly M3609)

0, 1, 4, 25, 174, 1393, 12536, 125361, 1378970, 16547641, 215119332, 3011670649, 45175059734, 722800955745, 12287616247664, 221177092457953, 4202364756701106, 84047295134022121, 1764993197814464540, 38829850351918219881, 893086558094119057262

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 A369325 A324169

Adjacent sequences: A006345 A006346 A006347 * A006349 A006350 A006351

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved