A001261 Number of permutations of length n with 5 consecutive ascending pairs.

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

Author

N. J. A. Sloane

Keywords

• nonn

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

Crossrefs

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

A diagonal in triangle A010027.

Programs

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 *)

Formula

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

Extensions

More terms from Vladeta Jovovic, Jan 03 2003

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