The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A169638 Number of multiset permutations of the n initial elements of A005229 with additional element A005229(0)=1. 2
1, 1, 1, 4, 20, 60, 420, 3360, 30240, 151200, 1663200, 9979200, 129729600, 1816214400, 27243216000, 217945728000, 3705077376000, 66691392768000, 633568231296000, 12671364625920000, 266098657144320000, 5854170457175040000, 134645920515025920000, 1615751046180311040000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
a(n) = number of permutations of the list b[0..n] where b(0)=0 and b(n) = A005229(n) for n>=1.
MAPLE
N:= 100: # to get a(0) to a(N)
A005229:= proc(n) option remember;
procname(procname(n-2))+procname(n-procname(n-2))
end proc:
A005229(1):= 1: A005229(2):= 1:
V:= Vector(N):
A[0]:= 1: V[1]:= 1:
for n from 1 to N do
r:= A005229(n);
V[r]:= V[r]+1;
A[n]:= A[n-1]*(n+1)/V[r];
od:
seq(A[i], i=0..N); # Robert Israel, Dec 23 2014
MATHEMATICA
Mallows[n_Integer?Positive] := Mallows[n] = Mallows[Mallows[n - 2]] + Mallows[ n - Mallows[n - 2]];
Mallows[0] = Mallows[1] = Mallows[2] = 1;
a[m_] := Length[Permutations[Table[Mallows[i], {i, 0, m}]]];
Table[a[m], {m, 0, 10}]
(* A much better way to compute the terms is to use the multinomials of the multiplicities of the terms of A005229! - Joerg Arndt, Dec 23 2014 *)
CROSSREFS
Cf. A169637.
Sequence in context: A355990 A169637 A356012 * A226424 A225260 A131479
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Apr 04 2010
EXTENSIONS
Edited and new name, Joerg Arndt, Dec 23 2014
a(11) to a(23) from Robert Israel, Dec 23 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 23 18:59 EDT 2024. Contains 372765 sequences. (Running on oeis4.)