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%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
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