login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A060523 Triangle T(n,k) = number of degree-n permutations with k even cycles, k=0..n. 4
1, 1, 0, 1, 1, 0, 3, 3, 0, 0, 9, 12, 3, 0, 0, 45, 60, 15, 0, 0, 0, 225, 345, 135, 15, 0, 0, 0, 1575, 2415, 945, 105, 0, 0, 0, 0, 11025, 18480, 9030, 1680, 105, 0, 0, 0, 0, 99225, 166320, 81270, 15120, 945, 0, 0, 0, 0, 0, 893025, 1596105, 897750, 217350, 23625, 945, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,7

REFERENCES

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, p. 189, Exercise 3.3.13.

LINKS

Alois P. Heinz, Rows n = 0..140, flattened

FORMULA

E.g.f.: (1+x)^((1-y)/2)/(1-x)^((1+y)/2).

EXAMPLE

Triangle T(n,k) begins:

1;

1, 0;

1, 1, 0;

3, 3, 0, 0;

9, 12, 3, 0, 0;

45, 60, 15, 0, 0, 0;

225, 345, 135, 15, 0, 0, 0;

1575, 2415, 945, 105, 0, 0, 0, 0;

11025, 18480, 9030, 1680, 105, 0, 0, 0, 0;

99225, 166320, 81270, 15120, 945, 0, 0, 0, 0, 0;

893025, 1596105, 897750, 217350, 23625, 945, 0, 0, 0, 0, 0;

...

MAPLE

with(combinat):

b:= proc(n, i) option remember; expand(`if`(n=0, 1, `if`(i<1, 0,

      add(multinomial(n, n-i*j, i$j)*(i-1)!^j/j!*b(n-i*j, i-1)*

      `if`(irem(i, 2)=0, x^j, 1), j=0..n/i))))

    end:

T:= n-> (p-> seq(coeff(p, x, i), i=0..n))(b(n$2)):

seq(T(n), n=0..12);  # Alois P. Heinz, Mar 09 2015

MATHEMATICA

nn = 6; Range[0, nn]! CoefficientList[

   Series[(1 - x^2)^(-y/2) ((1 + x)/(1 - x))^(1/2), {x, 0, nn}], {x, y}] // Grid  (* Geoffrey Critzer, Aug 27 2012 *)

CROSSREFS

Cf. A060524.

Sequence in context: A299904 A221768 A283071 * A199041 A199237 A309651

Adjacent sequences:  A060520 A060521 A060522 * A060524 A060525 A060526

KEYWORD

easy,nonn,tabl

AUTHOR

Vladeta Jovovic, Apr 01 2001

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 22 01:28 EST 2022. Contains 350481 sequences. (Running on oeis4.)