A105072 - OEIS

%I #14 Oct 07 2013 00:53:57

%S 1,2,5,16,63,290,1511,8756,55761,386394,2889181,23152104,197714479,

%T 1790887562,17136276943,172602398812,1824364931681,20179983080754,

%U 233031648587509,2803140527987776,35055393201882847,454955691827090802

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

%D Goulden & Jackson, Enumerative Combinatorics section 5.2.

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

%F 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

%F 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

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

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

%o (PARI)

%o N=66;  x='x+O('x^N);

%o egf=exp((6*x-1+exp(2*x))/4);  Vec(serlaplace(egf))

%o /* _Joerg Arndt_, Mar 07 2013 */

%K nonn

%O 1,2

%A _Louis Shapiro_, Apr 06 2005

%E More terms from _Robert G. Wilson v_, Apr 09 2005