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 A001260 Number of permutations of length n with 4 consecutive ascending pairs. (Formerly M3999 N1657) 6
 0, 0, 0, 0, 1, 5, 45, 385, 3710, 38934, 444990, 5506710, 73422855, 1049946755, 16035550531, 260577696015, 4489954146860, 81781307674780, 1570201107355980, 31698434854748604, 671260973394676605, 14879618243581997745 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 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 Vincenzo Librandi, Table of n, a(n) for n = 1..200 FORMULA (n-1)*a(n) = (n+3)*(a(n-1)*n + a(n-2)*n - a(n-1) + 2*a(n-2)). E.g.f.: (for offset 4): (x^4/4!)*exp(-x)/(1-x)^2. - Vladeta Jovovic, Jan 03 2003 G.f.: (for offset 0): hypergeom([2, 5],[],x/(x+1))/(x+1)^5. - Mark van Hoeij, Nov 07 2011 Recurrence (for offset 5): (n-5)*a(n) = (n-5)*(n-1)*a(n-1) + (n-2)*(n-1)*a(n-2). - Vaclav Kotesovec, Mar 26 2014 a(n) ~ n! * exp(-1)/24. - Vaclav Kotesovec, Mar 26 2014 MAPLE a:=n->sum((n+2)!*sum((-1)^k/k!/4!, j=1..n), k=0..n): seq(a(n), n=2..19); # Zerinvary Lajos, May 25 2007 series(hypergeom([2, 5], [], x/(x+1))/(x+1)^5, x=0, 30); # Mark van Hoeij, Nov 07 2011 MATHEMATICA Drop[CoefficientList[Series[x^4/4! Exp[-x]/(1 - x)^2, {x, 0, 20}], x] Range[0, 20]!, 4] (* Vaclav Kotesovec, Mar 26 2014 *) CROSSREFS Cf. A010027, A000255, A000166, A000274, A000313, A001261. A diagonal in triangle A010027. Sequence in context: A272494 A185009 A125836 * A088505 A067403 A173292 Adjacent sequences:  A001257 A001258 A001259 * A001261 A001262 A001263 KEYWORD nonn AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Jan 03 2003 Name clarified and offset changed by N. J. A. Sloane, Apr 12 2014 STATUS approved

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Last modified October 23 14:10 EDT 2019. Contains 328345 sequences. (Running on oeis4.)