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Number of permutations of length n with 5 consecutive ascending pairs.
(Formerly M4273 N1786)
5

%I M4273 N1786 #26 Dec 19 2021 09:53:57

%S 0,0,0,0,0,1,6,63,616,6678,77868,978978,13216104,190899423,2939850914,

%T 48106651593,833848627248,15265844099324,294412707629208,

%U 5966764207952724,126793739418994416,2819296088257641741,65470320271760790078

%N Number of permutations of length n with 5 consecutive ascending pairs.

%D F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 263.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A001261/b001261.txt">Table of n, a(n) for n = 1..200</a>

%F E.g.f.: (x^5/5!)*exp(-x)/(1-x)^2. - _Vladeta Jovovic_, Jan 03 2003

%p a:=n->sum((n+3)!*sum((-1)^k/k!/5!, j=1..n), k=0..n): seq(a(n), n=2..19); # _Zerinvary Lajos_, May 25 2007

%t Range[0, 30]! CoefficientList[Series[x^5/5!*Exp[-x]/(1 - x)^2, {x, 0, 40}], x] (* _Vincenzo Librandi_, Apr 13 2014 *)

%Y Cf. A010027, A000255, A000166, A000274, A000313, A001260.

%Y A diagonal in triangle A010027.

%K nonn

%O 1,7

%A _N. J. A. Sloane_

%E More terms from _Vladeta Jovovic_, Jan 03 2003

%E Name clarified and offset changed by _N. J. A. Sloane_, Apr 12 2014