A001261 Number of permutations of length n with 5 consecutive ascending pairs. (Formerly M4273 N1786)

0, 0, 0, 0, 0, 1, 6, 63, 616, 6678, 77868, 978978, 13216104, 190899423, 2939850914, 48106651593, 833848627248, 15265844099324, 294412707629208, 5966764207952724, 126793739418994416, 2819296088257641741, 65470320271760790078

Offset

1,7

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

E.g.f.: (x^5/5!)*exp(-x)/(1-x)^2. - Vladeta Jovovic, Jan 03 2003

Maple

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

Mathematica

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

Crossrefs

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

A diagonal in triangle A010027.

Sequence in context: A039937 A134112 A071588 * A252813 A346581 A210987

Adjacent sequences: A001258 A001259 A001260 * A001262 A001263 A001264

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Jan 03 2003

Name clarified and offset changed by N. J. A. Sloane, Apr 12 2014

Status

approved