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A105072 Number of permutations on [n] whose local maxima are in ascending order. 0
1, 2, 5, 16, 63, 290, 1511, 8756, 55761, 386394, 2889181, 23152104, 197714479, 1790887562, 17136276943, 172602398812, 1824364931681, 20179983080754, 233031648587509, 2803140527987776, 35055393201882847, 454955691827090802 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 21 17:29 EDT 2021. Contains 343156 sequences. (Running on oeis4.)