login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A010030 Irregular triangle read by rows: T(n,k) (n >= 1, 0 <= k <= [n/2]) =  number of permutations of 1..n with [n/2]-k runs of consecutive pairs up and down (divided by 2). 3
1, 1, 0, 3, 0, 3, 8, 1, 25, 28, 7, 17, 155, 143, 45, 259, 1005, 933, 323, 131, 2770, 7488, 7150, 2621, 3177, 27978, 64164, 62310, 23811, 1281, 51433, 294602, 619986, 607445, 239653 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

REFERENCES

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 264.

LINKS

Table of n, a(n) for n=1..35.

FORMULA

G.f. for number of permutations of 1..n by number of runs of consecutive pairs up and down is Sum(n!*(((1-y)*(2*x^2-x^3)-x)/((1-y)*x^2-1))^n,n = 0 .. infinity), cf. A010029. - Vladeta Jovovic, Nov 23 2007

EXAMPLE

Triangle begins:

1,

1, 0,

3, 0,

3, 8, 1,

25, 28, 7,

17, 155, 143, 45,

259, 1005, 933, 323,

131, 2770, 7488, 7150, 2621,

3177, 27978, 64164, 62310, 23811,

1281, 51433, 294602, 619986, 607445, 239653,

...

CROSSREFS

Cf. A002464, A001266, A000239, A000544, A001282.

Sequence in context: A021771 A154853 A139214 * A197270 A117940 A099093

Adjacent sequences:  A010027 A010028 A010029 * A010031 A010032 A010033

KEYWORD

tabf,nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vladeta Jovovic, Nov 23 2007

Entry revised by N. J. A. Sloane, Apr 14 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 21 20:51 EDT 2018. Contains 316428 sequences. (Running on oeis4.)