The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000313 Number of permutations of length n with 3 consecutive ascending pairs. (Formerly M3633 N1477) 9
 0, 0, 0, 1, 4, 30, 220, 1855, 17304, 177996, 2002440, 24474285, 323060540, 4581585866, 69487385604, 1122488536715, 19242660629360, 348933579412440, 6673354706262864, 134252194678935321, 2834212998777523380, 62651024183503148470, 1447238658638922729580 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Temporary remark: there may be some issues with respect to the offset of this sequence in the formula and program sections. - Joerg Arndt, Nov 16 2014 REFERENCES F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 263. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Todd Silvestri, Table of n, a(n) for n = 1..450 (first 100 terms from T. D. Noe) FORMULA a(n) = (n*(n+1)!/6)*sum((-1)^k/k!, k=0..n). a(n) = A065087(n+2)/3. - Zerinvary Lajos, May 25 2007 E.g.f.: x^3/3!*exp(-x)/(1-x)^2. - Vladeta Jovovic, Jan 03 2003 a(n) = round( (exp(-1)*(n+1)!+(-1)^n)*n/6 ). - Mark van Hoeij, Oct 25 2011 G.f.: hypergeom([2, 4],[],x/(x+1))/(x+1)^4. - Mark van Hoeij, Nov 07 2011 a(1) = 0, a(n) = (n-2)*(n-1)*(!(n-2))/6 = (n-2)*(n-1)*A000166(n-2)/6, for n >= 2. - Todd Silvestri, Nov 15 2014 a(n) = hypergeom([4-n,2],[],1))*(-1)^n*A000292(n-3). - Peter Luschny, Nov 19 2014 MAPLE series(hypergeom([2, 4], [], x/(x+1))/(x+1)^4, x=0, 30); # Mark van Hoeij, Nov 07 2011 a := n -> simplify(hypergeom([4-n, 2], [], 1))*(-1)^n*(n-1)*(n-2)*(n-3)/6: seq(a(n), n=1..23); # Peter Luschny, Nov 19 2014 MATHEMATICA Table[(n*(n + 1)!/6)*Sum[(-1)^k/k!, {k, 0, n}], {n, -1, 25}] (* T. D. Noe, Jun 19 2012 *) a[1]:=0; a[n_Integer/; n>=2]:=(n-2) (n-1) Subfactorial[n-2]/6 (* Todd Silvestri, Nov 15 2014 *) PROG (Sage) a = lambda n: (n-2)*(n-1)*sloane.A000166(n-2)/6 if n>2 else 0 [a(n) for n in range(1, 24)] # Peter Luschny, Nov 19 2014 CROSSREFS Cf. A010027, A000255, A000166, A000274, A001260, A001261. A diagonal in triangle A010027. Sequence in context: A134093 A007905 A084976 * A082144 A220727 A137971 Adjacent sequences:  A000310 A000311 A000312 * A000314 A000315 A000316 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Jan 03 2003 Formula added by Sean A. Irvine, Nov 11 2010 Name clarified and offset changed by N. J. A. Sloane, Apr 12 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 18 15:30 EST 2020. Contains 332019 sequences. (Running on oeis4.)