A105072 Number of permutations on [n] whose local maxima are in ascending order.

1, 2, 5, 16, 63, 290, 1511, 8756, 55761, 386394, 2889181, 23152104, 197714479, 1790887562, 17136276943, 172602398812, 1824364931681, 20179983080754, 233031648587509, 2803140527987776, 35055393201882847, 454955691827090802

Offset

1,2

References

Goulden & Jackson, Enumerative Combinatorics section 5.2.

Links

Table of n, a(n) for n=1..22.

Formula

E.g.f.: exp((6*x-1+exp(2*x))/4)

G.f.: 1/G(0) ; G(k) = 1 - 2*x*(k+1) - x^2*(k+1)/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Dec 19 2011

G.f.: 1/Q(0) where Q(k) = 1 - x*k - x - x/(1 - x*(k+1)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 07 2013

Example

a(3) = 5 since we have 123, 321, 231, 132 and 213 but not 312.

Mathematica

Range[0, 21]! CoefficientList[ Series[E^((6x - 1 + E^(2x))/4), {x, 0, 21}], x] (* Robert G. Wilson v, Apr 09 2005 *)

Prog

(PARI)
N=66;  x='x+O('x^N);
egf=exp((6*x-1+exp(2*x))/4);  Vec(serlaplace(egf))
/* Joerg Arndt, Mar 07 2013 */

Crossrefs

Sequence in context: A007124 A112951 A124470 * A022494 A136127 A111004

Adjacent sequences: A105069 A105070 A105071 * A105073 A105074 A105075

Keyword

nonn

Author

Louis Shapiro, Apr 06 2005

Extensions

More terms from Robert G. Wilson v, Apr 09 2005

Status

approved