|
| |
|
|
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; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
REFERENCES
| Goulden & Jackson, Enumerative Combinatorics section 5.2.
|
|
|
FORMULA
| E.g.f.: exp((6x-1+exp(2x))/4)
G.f.: A(x) = 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
|
|
|
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] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 09 2005)
|
|
|
CROSSREFS
| Sequence in context: A007124 A112951 A124470 * A022494 A136127 A111004
Adjacent sequences: A105069 A105070 A105071 * A105073 A105074 A105075
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Louis Shapiro (lshapiro(AT)howard.edu), Apr 06 2005
|
|
|
EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 09 2005
|
| |
|
|
