|
| |
|
|
A078483
|
|
Number of data structures of a certain wreath product type.
|
|
0
| |
|
|
1, 1, 2, 6, 20, 69, 243, 869, 3145, 11491, 42312, 156807, 584288, 2187298, 8221257, 31009841, 117331070, 445174418, 1693270531, 6454992143, 24657428519, 94363587324, 361741068087, 1388892123038, 5340282880156, 20560742443041, 79259430563491, 305889059254747
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
REFERENCES
| M. D. Atkinson and T. Stitt, Restricted permutations and the wreath product, Discrete Math., 259 (2002), 19-36.
|
|
|
FORMULA
| G.f.: -2*x/(1-5*x-(1-4*x)^(1/2)+x*(1-4*x)^(1/2)+2*x^2).
a(n) = the upper left term in M^n, where M is the following infinite square production matrix:
1, 1, 0, 0, 0, 0,...
1, 2, 1, 0, 0, 0,...
1, 1, 1, 1, 0, 0,...
1, 1, 1, 1, 1, 0,...
1, 1, 1, 1, 1, 1,...
...
- Gary W. Adamson, Jul 14 2011
a(n)=sum(m=1..n, m*sum(k=1..n-m, ((sum(j=0..m+k, binomial(j,-2*m-k+2*j)*binomial(m+k,j)))* binomial(n-m-1,k-1))/(m+k)))+1. [From Vladimir Kruchinin, Oct 11 2011]
|
|
|
PROG
| (Maxima)
a(n):=sum(m*sum(((sum(binomial(j, -2*m-k+2*j)*binomial(m+k, j), j, 0, m+k))*binomial(n-m-1, k-1))/(m+k), k, 1, n-m), m, 1, n)+1; [From Vladimir Kruchinin, Oct 11 2011]
|
|
|
CROSSREFS
| Sequence in context: A082679 A094854 A026029 * A163135 A047036 A199248
Adjacent sequences: A078480 A078481 A078482 * A078484 A078485 A078486
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 04 2003
|
| |
|
|
